Comments by "Fhf Fhf" (@fhffhff) on "MrGEO" channel.

  1. 601+2/3+1/3=602
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  2. (X-1)⁴-10(x-1)²+24(x-1)-27=0, (z-1)(z²-4z+9)=0 z=1;2±√5i x=±√10✓
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  3. (x-1)⁴-10(x-1)²+32(x-1)-7=0 (z-5/3)³-1/3(z-5/3)-11 25/27=0 z=5/3+(161+72√5)¹/³/3+(..-..)..; 5/3-(161+72√5)¹/³/6-(..-..)..±√(3/4 ((161+72√5)¹/³/3+(..-..)..)²-1/3)i x=-1±√5
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  4. {x+y=a,xy=b;{a³-15a+18=0,b=0,5a²-2,5; a=(-9+√(81-5³))¹/³+(..-..)..=2√5cos (1/3arccos(-9/5/√5)+2/3πn) b=10cos²(1/3arccos(-9/5/√5)+2/3 πn)-2,5 {y=√5cos(1/3arccos(-9/5/√5)+2/3πn)-+√(-2,5cos(2/3arccos (-9/5/√5)+4/3πn)),x=√5cos(1/3arc cos(-9/5/√5)+2/3πn)±√(-2,5cos (2/3arccos(-9/5/√5)+4/3πn)).n=0;2 x⁷+y⁷=129;(√5cos(1/3arccos(-9/5/√5)+4/3π)+√(-2,5cos(2/3arccos(- 9/5/√5)+8/3π)))⁷+(√5cos(1/3arcco s(-9/5/√5)+4/3π)-√(-2,5cos(2/3arc cos(-9/5/√5)+8/3π)))⁷
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  5. 30^(1/log2(30))=2
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  6. a/(a+b)*c,/_1/2,/_1/2+/_2 (c²+2ab (1+cos/_1))/2/(a+b)/cos0,5/_1-r(1/sin0,5/_1-1)≠a/(a+b)*c/sin/_3*sin(/_1/2+/_2)
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  7. X≤1 0=x⁴+6x²-40 x²=-3±7=4;-10 x=±2{-2}
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  8. (1 1 1|14) (0 5/2 -1|11/2) (0 0 1|96/13){Y=67/13,x=6/13.{(6/13;67/13;96/13)}
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  9. √(6-2x)=2x≥0,±5/4=x+1/4 x=✓1;-1,5×
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  10. {y=10-x,[x=8,x=2;{(2;8)(8;2)}
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  11. X=(√13-√5)/4 (-11'207'141+1'390'142√65)/64✓
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  12. (2x²-19x+42)(x²-7x+11)/(x-2)/(x-5)/(x-3)/(x-4)=0 [x=5,5,x=4,x=(7±√5)/2.
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  13. {z=(x³+16)/x/y,y=(x³+19)¹/³, [x=-8/3,x=2;{(2;3;4)(-8/3;1/3;-7 1/3)}
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  14. Sin80°/sin40°=2cos40° √(2-2cos40°)=2sin20° 2=1/sinx x=30°;150°(0;110°) x=30°✓
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  15. 6*1,5²-5*1,5+4=10
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  16. f(x)=64x⁵-40x³+5x✓
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  17. e^(e^(0,5x¹/³lnx)lnx)e^(0,5x¹/³lnx)(x¹/³(lnx+3)lnx+6)x-¹/6=0 x(e-³;1), 1/3x-²/³(ln²x+9lnx+9)=0 x=e^(-4,5±3√5/2)°0+*-*+>x min=e^(-1,5+√5/2)(18-9√5)+6~-62 65/127/113+5>0/> x=2^n n*2^(n/2*2^(n/3))=16,58*2^(8,29*2⁵,⁵²(⁶))/> x=2^16,58✓
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  18. ((x-127,5)²+5/12)³-1/3((x-127,5)²+5/12)-18 2/27=0 x=127,5±√(-5/12+(244+63√15)¹/³/3+(..-..)..)✓
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  19. 0,5(1/(1²-1+1)-1/(1²+1+1)+1/(2²- 2+1)-1/(2²+2+1)+..+1/(50²-50+1)-1/(50²+50+1))=1275/2551
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  20. (2x²-5x-3)(2x²-3x-5)=0 x=(5±7)/4;(3±7)/4{3;-0,5;2,5;-1}
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  21. [0=x³⁴-140x³⁰+8400x²⁶-280'000x²²+5600'000x¹⁸-21*32*10⁵*x¹⁴+(448*10⁶-1)*x¹⁰-100x⁸-160004*10³x⁶-80000x⁴-8*10⁵x²-20⁵,x=0;x=-0,59;-0,29;0,643{0;±0,802}
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  22. 0=x⁴+5x³+x²-18x-24 x=2;-4
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  23. X=(√17-√5)/6 (517-56√85)/27 (517+56√85)/27 1034/27✓
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  24. f(x+1/3/x)=3((x+1/3/x)⁵-5/3(x+1/3/x)³+5/9(x+1/3x-¹)) f(x)=3x⁵-5x³+5/3x f(2)=59 1/3
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  25. (√X+1,5)⁴-22,5(√x+1,5)²+90 9/16=0 (√x+1,5)²=(22,5±12)/2=17,25;5,25 x=(47-3√85)/2;(15-3√21)/2
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  26. (2+√3)(√1,5+√0,5)=1,5√6+2,5√2 1,5√6-2,5√2 3√6✓
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  27. (X+0,5)⁴-15,5(x+0,5)²+37(x+0,5)-68 11/16=0
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  28. Х=(-а±√((а-2116)(а-1936)))/2+ 1012 а(-=;1936]U[2116;°) (a-2026)²-90²=n²,[{a=4052,n=2024;{a=2704,n=672;{a=2436,n=400;{a=2260,n=216;{a=2166,n=110;{a=2128,n=56;{a=2128,n=48;{a=2116,n=0;{a=2128,n=48;{a=2132,n=-56;{a=2166,n=-110;{a=2260,n=-216;{a=2436,n=-400;{a=2704,n=-672;{a=4052,n=-2024; 9×2=18
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  29. (√(R²-2)-√8)²+2=(√(R²-9)-6)²+3² 9/4+√2/3√(R²-2)=√(R²-9) 12 1/16+3√2/2√(R²-2)-7/9(R²-2)=0 R=√(9(9√2+√1513)²/28²+2) S=π(16643+162√3026)/28²(cm²)
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  30. X⁰,⁵=y,x=y²,dx=2ydy $2y²dy/(y²+1)²= arctgy-y/(y²+1) (arctg√x-√x/(x+1)) lnx-2En=1;∞(-1)^(n-1)/(2n-1)²x^(n- 1/2)+2arctg√x(0;∞)=∞
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  31. (√(R²-6,5²)-6)²+11,5²=R² 126-12√(R²-42,25)=0 R=√152,5
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  32. -17/42ln|x|-5/21ln|x+9|+1/14ln|x+16|+c
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  33. У меня, похоже,ОКР.
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  34. A1=1,a2=2,a3=24,an=(6a(n-1)²a(n-3)-8a(n-1)a(n-2)²)/a(n-2)/a/(n-3) q=0
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  35. f(xy+1)=xf(y)-f(x)+6,f(1)=-f(0)+6,f(1)=xf (0)-f(x)+6,-f(0)=xf(0)-f(x),f(x)=xf0+f0,f0= f0,✓,f(1)=1f0+f0,-f0+6=2f0,f0=2 fx=2x+2
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  36. 86400*0,005=432с
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  37. 365,2422/(12 7/19)=29,53018
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  38. ±√(AP²-l1²+((l2²-l1²)/BC-BC)²/4)-0, 5(l2²-l1²-BC²)/BC=x coso=(-+√(AP²-l1²+((l2²-l1²-BC²)/B C)²/4)(l2²-l1²-BC²)+0,5BC(l2²-l1²-BC ²)²+BC²(2AP²-2l1²))(±√((4AP²-4l1²)B C²+(l2²-l1²-BC²)²)+l2²-l1²-BC²)/AP/((4AP²-4l1²)BC)$(-+√(AP²-l1²+((l2²-l1 ²-BC²)/BC)²/4)(l2²-l1²-BC²)+0,5BC(l2 ²-l1²-BC²)²+BC²(2AP²-2l1²))(√((4AP ²-4l1²)BC²+(l2²-l1²-BC²)²)±(l2²-l1²-BC ²))/((4AP²-4l1²)BC)*(AP²-l1²+((l2²-l1 ²)/BC-BC)²/4)-⁰,⁵dAP(0;BC)=l2-l1
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  39. Х[2;8],у(х;8] y≥(4+102x)/(98-x) (x+2)²≥0 x≤78/11 $(2;78/11)(-1000 0/(x-98)-102-x)dx+$(78/11;8)(8-x) dx=-10000ln|x-98|-102x-x²/2(2;78/ 11)+8x-x²(78/11;8)=10'000ln(132/125)-543 29/121
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  40. (z³)²-2z³-8=0 z³=(2±6)/2=4;-2 z=4¹/³;-2¹/³. x=4¹/³-2/4¹/³=2²/³-2¹/³;-2¹/³+2²/³{2²/³-2¹/³}
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  41. 3/7,2/5 (29/35)/(29/35)=1 a=6 S∆=(6+14+15)*6=210
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  42. {2=a+b,-12=a-b;{(-5;7)}
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  43. X[0;3+√14),(x-1,5)⁴-18,5(x-1,5)²+76 9/16=0 (x-1,5)²=(18,5±6)/2=12,25; 6,25 x-1,5=±3,5;±2,5 x=5;-2;4;-1{5;4}
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  44. C/√3cisx=ccos2x 0=2cos²x-√3/3cosx-1 cosx=(√3±5√3)/12≥0 x=30° S∆=0,5*c√3/2*c/2=c²√3/8
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  45. Ei=0;n-1|(i/n;(i+1)/n)(e^(nx-i)/nx²-e^ (nx-i)/n²*2x+e^(nx-i)/n³*2)=Ei=0;n-1 e/n³*2i+(e-2)n-²=en-¹-2n-² 0✓
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  46. {xy=a,x+y=b;{a⁴b=90/a⁴,a³b(b²-3a)=42;
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  47. x(-∞;-3)U[1;3],0=(x+1)⁴-8(x+1)²+x+1+12 (z-4/3)³-13/3(z-4/3)-5935/64/27=0 z-4/3=(5935/128+√(5935²/128²-13 ³))¹/³/3+(..-..)..=2/3√13cos(1/3arcc os(5935/128/13/√13)+2/3πn) z=4/3+2/3√13cos(1/3arccos(593 5/128/13/√13)+2/3πn) x=-1-√(4/3+2/3√13cos(1/3arccos (5935/128/13/√13)))+√(4/3+2/3√ 13cos(1/3arccos(5935/128/13/√ 13)+2/3π))+√(4/3+2/3√13cos(1/3 arccos(5935/128/13/√13)+4/3π)) ×;-1+√..-√..+√..✓;-1+√..+√..-√..×;-1- √..-√...-√..✓ 47/128<0,8
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  48. 2+861/148'953,172 261/861,3+ 78/261,27/78,24/27 3✓ 173/347✓
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  49. {(1-12/(y+3x))√x=2
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  50. {[{a=-6,b=9;{a=2,b=1;[x=3,x=-1.✓
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  51. √(2x²-98)=l [x=7,x=√63.x>7{√63}
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  52. x=3+1/(4+1/x),x>0 x=±√12{√12}
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  53. 0=x^log2(5)-x²-1,log2(5)(x^(log2(5)- 2)-2log5(2))x=0,x=0;(2log5(2))^(log(5/4)2)*-*+>x,min=(2log5(2))^log(5/4)5-(2log5(2))^(log(5/4)4)-1=-1,05..<0{2}
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  54. {а5=2,а4=3,А1=5,а2=6,А3=9;а1а2а3а4а5=56932
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  55. √(12,5²-25r)/(12,5-r)=7/25 0=-5,76+576/625r+49/125²r² r=12/(49/25)=300/49 b=arccos(4/5)+arcsin(24/175)=arcsin(3√(151*199)/875+96/875)
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  56. PQ=2/3√3
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  57. 0=42-х¹/⁴-14√х+х (z-7/3)³-175/12(z-7/3)-36'875/64/27=0 z-7/3=(295/2+√(295²-7³*128*2)/2)¹/³*5/12+(..-..)..=5/3*7⁰,⁵cos(1/3 arccos(295/112/√7)+2/3πn) 3,8/112<0,04 z=7/3+5/3*7⁰,⁵cos(1/3arccos (295/112/√7)+2/3πn) x¹/⁴=√(7/3+ 5/3*7⁰,⁵cos(1/3arccos(295/112/√7)))+√(7/3+5/3*7⁰,⁵cos(1/3arcco s(295/112/√7)+2/3π))+√(7/3+5/3* 7⁰,⁵cos(1/3arccos(295/112/√7)+4/ 3π))✓;-√-√+√×;-√+√-√×;√-√-√✓ x=(√(7/3+ 5/3*7⁰,⁵cos(1/3arccos(295/112/√7)))-√(7/3+5/3*7⁰,⁵cos(1/3arcco s(295/112/√7)+2/3π))-√(7/3+5/3* 7⁰,⁵cos(1/3arccos(295/112/√7)+4/ 3π)))⁴✓
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  58. X=(15±9)/800=0,03;3/400
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  59. 34/(38/(47*9/28-9)-35/9)-9(cm) ?=39(cm²)
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  60. a=0,5arcsin0,6(-1)^n+πn/2 b=a-30°;150°-2πm=0,5arcsin0,6-π/6 +π(n-2m);0,5arcsin0,6-5/6π+π(n-2m);π/3-0,5arcsin0,6+π(n-2m);-π/3-0,5 arcsin0,6+π(n-2m) sin(a+b)=0,6;-0,3√3-0,4;0,4±0,3√3
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  61. -5b*5b+(3c-4a)²=(3c-4a-5b)(3c-4a+ 5b)
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  62. 0,5/_1+82°+2(85°-/_1)=180° /_1= 48° ?=180°-24°-37°=119°
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  63. 9²+9*25+25²=931
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  64. 0=(8^x)³-8*8^x-32 x=1/3+log8((2+10√3/9)¹/³+(..-..)..)= 2/3 1,58+0,43=2,01 1/3, 10/9√3✓
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  65. $(1/3;3)arctgx/(x²-x+1)dx=$(1/3;3)(π/2-arctgx)/(1-x+x²)dx=$(1/3;3)π/4/(x²-x+1)dx=π/2arctg((x-0,5)/√3* 2)/√3(1/3;3)=π/2/√3(π/3+arctg(√ 3/9))
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  66. |8-|х-2||=7,8-|х-2|=±7,{|х-2|=1,|х-2|=15;{х-2=±1,х-2=±15;[х=3,х=1,х=17,х=-13
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  67. f(x)²+f(x)f(1)-1=0 f(x)=(-f(1)±√(f(1)²+4))/2=±√2/2
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  68. X^(1+1/r)e^(ln(1+1/x)/(1-1/(1+1/x) ^(r+1)))=xe^(ln(1+1/x)(1+x)) e✓
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  69. (√2+1)³+(√2-1)³=10√2
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  70. 5^x=3^xlog(3)5,(5/3)^x=log(3)5,x=log (5/3)log3(5)
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  71. 5^x=5³(63±62)=5⁶;5³ x=6;3{(6;3)(3;6)}
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  72. 2^(2n-5)*e^(Ei=1;=(-1)^in/πsin(π/n)/i3^i((cos(π/n))^(2i-1)*2^(2i-2)(i-1)!²/(2i-1)!+2^(2i-4)(i-2)!²/(2i-3)!cos(π/n)^ (2i-3)+..+1/2^i/i!cos(π/n)-(N-1)π/n/2/sin(π/n))(2i-1)!!/(2i)!!+0,5ln(3cos² (π/n)+1)) n✓
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  73. X¹/⁴=y,x=y⁴,dx=4y³dy $√2dy(1/(y+ 1)/(1-√2y+y²)-1/(y+1)/(1+√2y+y²))= -2ln|y+1|-(√2-1)/2ln|y²-√2y+1|+arctg ((y+√2/2)√2)+(√2+1)/2ln|y²+√2y+1| -arctg((y+√2/2)√2)(0;∞)=π 1=A(1-√2y+y²)+B(y+1)(2y-√2)+C(y+ 1) {A=(2-√2)/2,B=-(2-√2)/4,C=1/2; -1=A(1+√2y+y²)+B(y+1)(2y+√2)+C (y+1) {A=-(2+√2)/2,B=(2+√2)/4,C=-1/2;
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  74. X≥-1 [{0=x⁵/³+4x⁴/³+11,5x+21,5x²/³+29x¹/³+32,x[-1;0);x=1;{1}
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  75. S∆=√3*10=4h h=2,5√3 S=(2+10)/2*2,5√3=15√3
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  76. p(lnp+if)=ln4+i(π/3+2πn){p=2,f=π/6+πn;z=±(√3+i)
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  77. -x²⁰²²+2024=-1+2024=2023
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  78. 4^(5/(x-5))=4-¹ x=0✓
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  79. 12=2^(x³-6)+x³/> x³=8✓,x=2✓
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  80. 4+8√3-4√3*ctga=AB,4cosa/sina* ((1+2√3)sin2a-cos2a√3)=x atcsin(±(2+√3)/2/√(4+√3))/2+1/2arccos((1+2√3)/2/√(4+√3));π/2-atcsin(±(2+√3)/2/√(4+√3))/2+arccos((1+2√3)/2/√(4+√3))/2+πn=a,a=75°,x=(8-4√3)(2-√3)=28-16√3
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  81. F(x)=0,5(arctgx-arctg(1-1/x)-π/2+arctg(x-1)) -3π/8✓😊
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  82. (52+6√43)(√43+3)+(52-6√43)(√43- 3)=140√43
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  83. PQ=√2/2PS/sin3/_R PR=√2/2PS/si n/_R √2/2PSctg3/_R+√2/2PS=QS= √2/2PSctg/_R-√2/2PS 0=(tg/_R+ 1/3)³+3 1/3(tg/_R+1/3)-4/27 tg/_R +1/3=(2+2√251)¹/³/3+(2-2√251)¹/³/3 /_R=arctg(-1/3+(2+2√251)¹/³/3 +(2-2√251)¹/³/3)✓
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  84. (sin8x+sin3x)cosx=0[x=π/2+πn,sin8x= sin-3x;8x=-3x+2πn,=π+3x+2πn x=2/11πn; π/5+2/5πn{π/2+πn;2/11πn; π/5+2/5πn}
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  85. (1+1/3)/(1-1/3)=2 (n+1/(n²+n+1))/(1-n/(n²+n+1))=n+1 π/2✓
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  86. 10√(25+12√3) 83°-arcsin(1,5/√(25 +12√3)) 10√(50-40cos83°+12√3-30 sin143°)✓
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  87. √(9+a²+3a) arcsin(a/√(9+a²+3a)√ 3/2),60°-arcsin(a/√(9+a²+3a)√3/2) a²=9 a=3 y=3√3,R=3✓
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  88. (2-y)⁵+y⁵=32-80y+80y²-40y³+10y⁴ {√x=16-40y+40y²-20y³+5y⁴,√(x+32)=16-40y+40y²-20y³+5y⁴-y⁵; 0=y¹⁰-10y⁹+40y⁸-80y⁷+80y⁶-32y⁵-32 0,2+2(y-1)²+(y-1)⁴≥0 (y-1)((y-1)⁴+10(y-1)²+5)≤0 y≤1 y=1-√3,x=76²=5776{(5776;1-√3)}
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  89. {(x²/³+y²/³)²-2x²/³y²/³=17,(x²/³+y²/³)((x²/³+y²/³)²-3x²/³y²/³)=65;{x²/³+y²/³=a,x²/³y²/³=y;{b=0,5a²-17/2,a³-51a+130=0;a=(-65+√(65²-17³))¹/³+(..-..)..=2√17cos (1/3arccos(-65/17/√17)+2/3πn), b=34cos²(1/3arccos(-65/17/√17)+ 2/3πn)-8,5{y=±(√17cos(1/3arcco s(-65/17/√17)+2/3πn)-+√(-8,5cos (2/3arccos(-65/17/√17)+4/3πn))) ¹,⁵, x=±(√17cos(1/3arccos(-65/17/√17)+2/3πn)±√(-8,5cos(2/3arcco s(-65/17/√17)+4/3πn)))¹,⁵,n=0;2.
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  90. X>0 \>=/> (7+5√2)^x-¹=x³ x(1,5;2)(3+2√2?27/8) x=1,69..✓
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  91. S=1/3πR²+R²√3/4 p=1/3+√3/4/π
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  92. (x-2/27)³-4/243(x-2/27)-259/3⁹=0 x=2/27+(259/2+45√33/2)¹/³/27+(..-..)..=1/3✓
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  93. amF/M/I=t,I=1 A t=0,6552(с)
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  94. y³-3x²y+2x3-16=0 y=(-x³+8+4√(-x³+4))¹/³+(..-..)..{(-1;3)(5;6)(2;0)}
    1
  95. {(-2,4;5,25;-15/7)(1;1;10)(-2;7;-2)}
    1
  96. {b≤30-a,b=17-a,[a=12,a=5;c=13
    1
  97. гл(а)(а).. Нет б,е,и,й,к,п,р,с,т,у,ф,ы. Гладь!
    1
  98. {(x+1-√(1-a))(x+1+√(1-a))≤0,+*+>x (x-2-√(4+6a))(x-2+√(4+6a))≤0+*+>x;{x[-1-√(1-a);-1+√(1-a)],x[2-√(4+6a);2+√(4 +6a)];a≤1,a≥-2/3,a[-2/3;1] -1-√(1-a)≤2+√(4+6a) [{x[-1-√(1-a);-1+√+1-a)],a[-1;0),x[2-√(4+6a);-1+√(1-a)],a[0;1].
    1
  99. {y=(4a+1)/(a²+5a+15),[a=0, x=(a-55)/2/(a²+5a+15). a²-7a+12=0 a=3;4✓
    1
  100. {y=(26-x^(2x))^(0,5/x),x^(2(26-x^(2 x))^(0,5/x))+(26-x^(2x))^((26-x^(2x)) ^(0,5/x)/x)=5,x^(x+(26-x^(2x))^(0,5/x))+(26-x^(2x))^((x+(26-x^(2x))^(0, 5/x))/2/x)=7;{x=2,1322,y=0,9349; 2,9601~✓
    1
  101. (2x+6)²+(9x+6)²=169x² -7x²+11x+6=0 x=(-11±17)/-14=-3/7;2>0 S=0,5*10*24-0,5*4*18=84(cm²)
    1
  102. X1=x2+x3,х-1+х-2+х3=-b, x1x2+x1x3+x2x3=c, x1x2x3=-d,x1=-b/2, b²/4+x2x3=c, x2x3=-d/-b*2, c-b²/4=2d/b, -x2²-b/2*x2+b2/4-c=0, x2=(0,5b+√(0,25b²-4(-1)(b²/4-c)))/(-2), x3=-025+0,5√(1,25b²-4c),
    1
  103. |√(х-1)-2|+|√(х-1)-3|=1 √(х-1)[2;3] х-1[4;9],х[5;10]
    1
  104. 2/3√3 2/3√3/(4/3√3)=1/2 arctg(1/3) 4/3√1,5 S∆=8/3√0,5
    1
  105. X³-2x-1=0[x=-1,x²-x-1=0;x=(1±√5)/2 {-1;(1±√5)/2}
    1
  106. (R-r)²+288/π=(R+r)² 72/π=Rr, R-r=√(72/π){-√(18/π)+√(90/π)=r, R=√(18/π)+√(90/π);S=π/2(R²+r²)=π/2(216/π)=108
    1
  107. Х=√3/2±1/2i x¹⁰⁰⁰=-1/2±√3/2i -1✓
    1
  108. 1¹2³820²5*4=512820(✓?)
    1
  109. X=2(cos(π/4+πn/2)+isin(π/4+πn/2))
    1
  110. -1+а²/(a²-b²)=b²/(a²-b²)
    1
  111. Arccos(15/8/√13),AC*7/12, arccos(13/14) AC=(13√607+45√3)/2/√39, x=AC*7/12-4=14,7E)
    1
  112. (3¹/²-1)/16✓
    1
  113. 108√5=13,5h h=8√5 r=4√5 8√5/21=2tg0,5a/(1-tg²0,5a) 4√5/21-tg0,5a-4√5/21tg²0,5a=0 tg0,5a=(-21+√761)/(8√5) (21+√761)/2 (21+√761)²/4=l(l-x), (9,5-√761/2)²=(√720-l)(√720-l+x) {2√(-42-2√761)/3=x✓, l=(37√5+√5√761+2√(-42-2√761))/6.√(-42-2√761)≥2/9
    1
  114. e^x-x=0, e^x-1=0, x=0, -*+ минимум 1 т.е. решений не существует
    1
  115. (x³/18-3/2)³=9(2x+3) 0,5((x³/18-3/2) ²*x²-36)=0 x⁴-27x-+108=0 z³±27/2z-729/64=0 z=(1/2+√2049/2)¹/³*9/4+(...-..)..;- (1/2+√2049/2)¹/³*9/8-(...-..)..±√(3/4 ((1/2+√2049/2)¹/³*9/4+(...-..)..)²+2 7/2)i z=9*2¹/²cos(1/3arccos(1/32/√2)+2/3πn) x=√((1/2+√2049/2)¹/³* 9/4+(...-..)..)±2√(0,5√(((1/2+√2049/ 2)¹/³*9/4+(...-..)..)²+27/2)-(1/2+√204 9/2)¹/³*9/16-(...-..)..) ×+*+>x max=((√((1/2+√2049/2)¹/³*9/4+(...-..)..)-2√(0,5√(((1/2+√2049/2)¹/³*9/4+(...-..)..)²+27/2)-(1/2+√204 9/2)¹/³*9/16-(...-..)..))³/18-1,5)³-18 (√((1/2+√2049/2)¹/³*9/4+(...-..)..) 2√(0,5√(((1/2+√2049/2)¹/³*9/4+(...-..)..)²+27/2)-(1/2+√2049/2)¹/³ 9/16-(...-..)..))-27?0 min=((√((1/2+√2049/2)¹/³*9/4+(...-..)..)+2√(0,5√(((1/2+√2049/2)¹/³*9/4+(...-..)..)²+27/2)-(1/2+√204 9/2)¹/³*9/16-(...-..)..))³/18-1,5)³-18 (√((1/2+√2049/2)¹/³*9/4+(...-..)..)+ 2√(0,5√(((1/2+√2049/2)¹/³*9/4+(...-..)..)²+27/2)-(1/2+√2049/2)¹/³* 9/16-(...-..)..))-27<0 3 решения х=4,85;-1,85;-3✓
    1
  116. {x=1000-2018y-¹,1000y²-3009y+2018=0;y=(3009±991)/2000=2;1,009 x=991;-1000{(991;2)(-1000;1,009)}
    1
  117. a=a1³,2a1⁵+2a1⁴+2a1³+2a1²+2a1+2+2/(a1-1)=b,a1-1=±1;±2 a1=2:0;3;- 1 b=127;-2;729;-1 a=8;0;27;-1{(8;12 7)(0;-2)(27;729)(-1;-1)}
    1
  118. z=2+2i±i=2+3i;2+i
    1
  119. 2021/7=288 4/7 577? ходов
    1
  120. {x=z³-y²,[y=0,y=-1;z=0,z=1,z=(1±√5)/2;z=0,2z⁵-z³+z±√(z³-z)(z²-1)=0;[{z=0,yR;{z≠0,[y=z,y=±√(z³-z); 4z⁹-4z⁷-z⁶+5z⁵+3z⁴-2z³-3z²+z+1=0 36z⁸-28z⁶-6z⁵+25z⁴+12z³-6z²-6z+1=0 z[-1;0]U[1;≠)+ z=-0,43{(0;0;0)(-1;-1;0)(0;1;1)(1/2±√5/2;1/2±√5/2; 1/2±√5/2)(-0,43;-0,59;-0,43)}
    1
  121. 4+d²-2d√3=b²+4-2b√3 [b+d=2√3✓,b=d×.
    1
  122. AG/GB=GB/(4/9AG) 2/3AG=GB k=1,5 BF=18/1,5=12
    1
  123. (-1+√3)/2+(-√3+√5)/2=(-1+√5)/2 (-129+13√5)/2✓
    1
  124. Алзим:х+у.Ера:2020-х+у.х=1010?✓
    1
  125. (y')'/cosy'+1=0,$(y')'/sin(π/2-y')dx+x=C,ln|tg(π/4-y'/2)|+x=C,tg(π/4-y'/2)=±e^(-x+C), π/4-y'/2=arctg(Ce^-x)+πn,y=-2$arctg(C e^-x)dx+(π/2-2πn)x+c1
    1
  126. {z=2-x-y,2±√(8-(x-2)²)=y;✓
    1
  127. (3 -4|8) (0 1|1) ..=4{x=0,19,y=2/25.
    1
  128. 2sin55°/sin70°=1/siny siny=sin35° y=35°;145°<110° y=35° D)
    1
  129. 7/√193=x/√(x²+9) 7/4=x
    1
  130. En=0;∞C(1/3;2n)*2Ei=0;nC(n;i)((-1) ^i+(1/3)^(3i+1))/(3i+1)✓
    1
  131. X-1=±2(x-2),[x=3,x=5/3.
    1
  132. (1+cos2°)/sin2°✓
    1
  133. 1/√(1-x²)Ei=0;nC(n;i)(-1)^i(ln^(n+1-i)(1+x)/(n+1-i)ln^i(1-x)-$ln^(n+1-i)(1+ x)iln^(i-1)(1-x)/(x-1)dx)-$dx*x(1-x²)- ¹,⁵Ei=0;nC(n;i)(-1)^i(ln^(n+1-i)(1+x)/(n+1-i)ln^i(1-x)-$ln^(n+1-i)(1+ x)iln^(i-1)(1-x)/(x-1)dx)=∞
    1
  134. En=1;∞(-1)^(n-1)(x^(4n-3)/(4n-3)lnx- x^(4n-3)/(4n-3)²)/(2n-1)!|∞=?
    1
  135. у=75°-х, sin²x+sin²(75°-x)=3/4, (1-cos2x)/2+(1-cos(150°-2x))/2=3/4, cos2x+cos(150°-2x)=1/2,2cos75°cos(2x-75°)=1/2, cos(2x-75°)=1/4/√((√3-1)²/4),2x-75°=±arccos(0,25/(√3-1)*2)+2πn,nєZ, x=37,5±0,5arccos(0,25(√3+1))+πn,nєZ, y=37,5-+0,5arccos(0,25(√3-1))-πn, -√3/2=2²-1, =√((-√3/2+1)/2)
    1
  136. 2cos16,875°✓
    1
  137. (x/y)^(x-y)=2³ y=3,x=6✓
    1
  138. X-2y+(y-2x)i=5+i{x=-7/3,y=-11/3. z=-7/3-11/3i
    1
  139. X=(2±√10)/3{16}
    1
  140. S∆=24=2h,h=12 9+5=14 S=(4+14)/2*12=9*12=108
    1
  141. {x((a-A)x+b-B)≤0,x((a+A)x+b+B)≥0;|b²-4ac|≤|B²-4AC|
    1
  142. S=(√5+a)/2*√5+(a+b)/2*(a+b)-0,5 (√5+b)(√5+a+b)=10+√5b-√5b=10
    1
  143. Sin(14x)=sin(π/2-68x)[x=π/164+ 1/41πn,x=-π/108-1/27πn;x[0;2π) n[0;82],n[-54;0]
    1
  144. Хє[0;π/4]U[3/4π;5/4π]U[1,75π;2π) [x=π/4+πn,x=2πn,x=-π/2+2πn;{π/4; 5/4π;0}S∆=0,5*2sin22,5°*2cos22,5°=√2/2 A)
    1
  145. 2f(x)+f(1-x)=3x²,f(1-x)+0,5f(x)=1,5 (1-x)² f(x)=x²+2x-1✓ f(5)=34
    1
  146. (√2+1)^x=(√2±1)⁴ x=±4
    1
  147. 2π*0,5/2*2*4=4π
    1
  148. x=±2√5a/5
    1
  149. [{a(-1-√11,5;-1+√11,5),x=a+7;{x=-a+2,a(-1,5-√10,25;-1,5+√10,25).
    1
  150. (2R)²=a²+b²,R=0,5√(a²+b²) a+b=a+b✓,arct g(a/b),r/a*√(a²+b²)+r/b*√(a²+b²)=√(a²+b ²),r=ab/(b+a)
    1
  151. X=22/(3)-2-1/3=5
    1
  152. Arccos(23/27) tg(0,5arccos(23/27))*12=√((4/27)/(50/27))*12=12√2/5 S=288/25π
    1
  153. [x²+x-16=0,x²-x-15=0;[x=(-1±√65)/2, x=(1±√61)/2.
    1
  154. -sinxcos(2x)..cos(nx)+cosx((-2sin (2x)cos(3x)-3cos(2x)sin(3x))..cos(nx)+..)=-cosxcos(2x)..cos(nx)(tgx+2t g(2x)+..+ntg(nx))=0,x=π/2+πm;..;(π/2+πm)/n;?+*0->x f''(x)=cosxcos(2x)..cos(nx)((tgx+2t g(2x)+..+ntg(nx))²-cos-²x-cos-²(2x) -..-cos-²(nx))=0 f''(0)=-n n>2023
    1
  155. (x²-6x+a²+2a)/(2x²-ax-a²)=0,2 разл.реш. {х=(6±√(36-4(а²+2а)))/2,2х²-ах-а²≠0;{х=3 ±√(-а²-2а+9),х≠(а±√(а²-4*2*а²))/4=а/4± √9а/4;{х=3±√(-а²-2а+9),[х≠а,х≠-0,5а;-а²-2 а+9>0,(а-(2+√(4-4*-1*9))/-2)(а-(2-√4 0)/-2)<0,-1-√10+°-1+√10-°+>а,ає(-1-√10; 1+√10),3+√(-а²-2а+9)=а,√(-а²-2а+9)=-3 +а,{-а²-2а+9=9-6а+а²,-3+а≥0;{-2а²+4а=0, а≥3;{-2а(а-2)=0,а≥3;{[а=0,а=2,а≥3;0/3+√ (-а²-2а+9)=-0,5а,√(-а²-2а+9)=-3-0,5а≥0,{-а²-2а+9=9+3а+0,25а²,-3-0,5а≥0;{-1,25а²-5а=0,а≤-6;{[а=0,а=-4;а≤-6;0/ 3-√(-а²-2а+9)=а,√(-а²-2а+9)=3-а,а=0;2 3-√(-а²-2а+9)=-0,5а,√(-а²-2а+9)=3+0,5а,а=0;-4 ає(-1-√10;-4)U(-4;0)U(0;2)U(2;-1+√1 0)
    1
  156. S=√3/2-1/4π
    1
  157. Yx²-x+y³-3y=0 x=(1±√(-4y⁴+12y²+1))/2/y ±√(-4y⁴+12y²+1)=3y y=±1 x=(1±3)/±2=2;1{(2;1)(1;-1)}
    1
  158. y'=z,z"+2z'+z=0,k²+2k+1=0,k=-1,×2 z=c1 e^-x+c2xe^-x,y=-c1e^-x+c2x*-e^-x-c2^-x+c3=c1e^-x+c2xe^-x+c3
    1
  159. √(а²+9) 1/(0,5√(а²+9))=а/3 3⁰,⁵=а S=3√3
    1
  160. -81*?/280+41+11/140
    1
  161. En=1;≠*2(-1/(n+1)+1/n)=2
    1
  162. X≥7 (x-2)³-100(x-2)+288=0 x-2=(-144+8√(18²-25³/27))¹/³+(..-..)..=20/3¹/²cos(1/3arccos(-54/ 125√3)+2/3πn) x=2+20/3¹/²cos (1/3arccos(-54/125√3)),n=0 54√3<125,5 21/173×
    1
  163. [х+2=0,0=(х+2)⁴+90(х+2)²+810;{-2}
    1
  164. B=sin70°/sin30°*a ..=2sin80°a a(1+2sin70°)/sin110°=2sin80°a/sin? 40°=?
    1
  165. g(x)=14/(x+4)-3
    1
  166. 2sin0,5o(cos(-π/2+0,5o)+isin(-π/2+0,5o)) ln(2sin0,5o)+i(-π/2+0,5o+ 2πn),o(4πm;2π+4πm);ln(-2sin0,5o)+i(π/2+0,5o+2πn),o(2π+4πm;4π+4 πm)
    1
  167. -2sinx/cos7x/cos8x=2cos15xsinx [sinx=0,-5=cos30x+cos16x+cos14x; x=πn
    1
  168. (√6+√2)*(√6-√2)/2=2 S∆=0,5*2(2√3+2)sin120°=3+√3
    1
  169. (х²+27/2х+77)х=0 х=0;(-27±√503i)/4{0}
    1
  170. 1,5t+0,5=√(t²+3),t≥0 1,25t²+1,5t-2,75=0 t=(-1,5±4)/2,5= 1;-11/5≥0 √(x+6)=1,x=-5✓
    1
  171. (х-19/3)³-334/3(х-19/3)-451 2/27=0 х-19/3=(6089,5+√(6089,5²-334³))¹/³/3+(..-..)..=2/3√334cos(1/3arccos(60 89,5/√334³)+2/3πn) x=19/3+2/3√334cos(1/3arccos(60 89,5/√334³)+2/3πn) 77,5<92 7/9
    1
  172. 137-9n,n[9;∞) 9'999'995+999'999'995=1009'999'990 1+9*6=55
    1
  173. {х=(у²+3)/у,3(у²)²+14у²+18=0;у²=-7/3±√ -5/3,у=±6⁰,²⁵(√(-7√6+18)/6±i√(18+7√6)/6) х=±(-16√(-7√6+18)+√(90+35√6)±i(16 √(18+7√6)+√(-35√6+90)))6⁰,⁷⁵/108 xy= 6⁰,²⁵(117√6±i(-8√30+18√5))/324 Otvet:6⁰,²⁵(117√6±i(-8√30+18√5))/27=8.
    1
  174. a=2x-x³ x³-2x+a=0 x=(-a/2+√(a²/4- 8/27))¹/³+(..-..).. cos(1/3arccos(-a/2/√(8/27))=3a/4√1,5 4√3/9=a
    1
  175. ±х-2^(х/32)=0 1-2^(х/32)ln2/32=0 x=32log2(32/ln2)+*->x max=32log2(32/ln2/e)>0 x=256;1,03 x=-0,97{256;1,03;-0,97}
    1
  176. (2x-1)(3y+2)=33(2;3)
    1
  177. 3f(-x)+f(1/x)+f(x)=x,3f(-1/x)+f(x)+f(1/x)=1/x,3f(1/x)+f(-x)+f(-1/x)=-1/x,3f(x)+f(-1/x)+f(-x)=-x 3f(-x)+f(1/x)+f(x)=x,f(-x)-f(-1/x)= 1/3x-1/3/x,3/2f(1/x)+f(-1/x)=-x/6-1/3/x,f(x)=-1/3/x-2/3*x
    1
  178. ..>n(m-1)/2-m+1,≤n(m-1)/2 ..=[n(m-1)/2]..
    1
  179. 3^log0,6(log(3)5)-5^log0,6(log(3)5)≥3^x-5^x=4(x-0,75)²-2,25≥-2,25 1 koren x[0,75; ∞)х=1(-2=-2),хє[-log3(5);0,75)\>=\> х=0 x<log(0,6)log3(5),/>=\>x=-1,7 0/ {1;0}
    1
  180. 2√r1+2√(r1(3-2√2))=2√(3-2√2) r1=1,5-√2.
    1
  181. -√(x²-2)(x²-1)/2arcsin²(1/(x²-1))/2-x(3x²/2-2,5)(x²-1)/2*arcsin³(1/(x²-1))/6-...(√2; ∞)=√2(π/4)³/24+..
    1
  182. E..≥-ln²n+2lnn/n,≤-ln²n+2lnn/n-0,5n-¹+0,5 lim[n^(2+2/n)/n^n;n^(2,5+2/n)/n^n/n^(0,5 n-¹)]=0
    1
  183. (x-1)(x²-2x+4)=0[x=1,0/.
    1
  184. 0=5(x-31,5)⁴+2,5(x-31,5)²-30,937'5 x-31,5=±1,5 x=33;30✓
    1
  185. (3/2)^(2/9)✓
    1
  186. f(x)=ca^x a^(a^x)=e^-x,c=1×
    1
  187. -lnf(x)=f-¹(x) невозможно решить
    1
  188. x=i)-i+2πn)=1+2πni
    1
  189. (logx(3)-1)(logx(3)+1/3)/(logx(3)- 1/3)≤0-*-1/3+°1/3-*1+>logx(3) logx(3)(-∞;-1/3]U(1/3;1][x[1/27;1),[3;27];x[1/27;1)U[3;27]
    1
  190. X=√((5x-1)/(x-3)/(x-2)),x≥0 (x-1,25)⁴-2,75(x-1,25)²-5 5/8(x-1,25) 4 3/64=0 (z-11/24)³+41/48(z-11/24)+3'397'741/27/2¹⁸=0 z=11/24+(-3397741/2 +√(3397741²+41³*2²⁶)/2)¹/³/192+(..-..)..;11/24-(-3397741/2+√(33977 41²+41³*2²⁶)/2)¹/³/384-(..-..)..±√(3/ 4((-3397741/2+√(3397741²+41³* 2²⁶)/2)¹/³/192+(..-..)..)²+41/48)i x=1,25+√(11/24+(-3397741/2+√ (3397741²+41³*2²⁶)/2)¹/³/192+(..-..)..)+2√(0,5√(121/24²-11/24(( 3397741/2+√(3397741²+41³*2²⁶)/2)¹/³/192+(..-..)..)+((-3397741/2+√ (3397741²+41³*2²⁶)/2)¹/³/192+(.. -..)..)²+41/48)+11/48-(-3397741/2+√(3397741²+41³*2²⁶)/2)¹/³/768-(.. -..)..)
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  191. Sin(2t+32°)=-1/2 [t=-31°+πn,t=89°+πn.
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  192. (388-x²)¹/⁴+√x=5√2, (388-x²)¹/⁴x¹/²=50±38=88;12 [(x²-194)²=×194²-88⁴,x=18,x=8;{18;8}
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  193. $(0;2π)1/16(4,375-7cos2x+3,5cos4x-cos6x+0,125cos8x)dx=1/16(4,375x-7sin2x/2+3,5sin4x/4-sin6x/6+1/64 sin8x)(0;2π)=1/16(8,75π)=35/64π
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