Comments by "Fhf Fhf" (@fhffhff) on "TED-Ed" channel.

  1. (2cos²x-5cosx+2)log11(-sinx)=0,{-sinx>0, sinx<0,хє(-π+2πn;2πn),[2cos²x-5cosx+2 =0,-sinx=1;[cosx=(5±√(25-4*2*2))/4,sinx =-1;[cosx=2,cosx=1/2,x=-π/2+2πn;[x=±π/3+2πn,x=-π/2+2πn;[x=-π/3+2πn,x=-π/2+ 2πn;
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  2. √(8х+13)+√(2х-3)=5,{8х+13≥0,2х-3≥0;{х≥- 13/8,х≥1,5;х≥1,5. √(8*1,5+13)=5≥5,х=1,5.
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  3. U:I1*10,10I2,20(I1-I2),50(I-I1),50(I-I2). 4I1-2,5I=I2 I2=1/4I1+5/8I 5/6I=I1 R=16 2/3 Om 29 29/30 Om, I=3000/899A
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  4. (1-x/2)log(13-3*2^x)4≤1,{13-3*2^x>0,1 3-3*2^x≠1;{2^x<13/3,2^x≠4;{x<log(2)(13/3),x≠2;хє(-∞;2)U(2;log(2)13/3) (-x/2+1-log(4)(13-3*2^x))/log(4)(13-3*2^x)≤0, 1/2-1/(13-3*2^x)*-3*2^x*ln2/ln4=0,-1/2 +3/(13-3*2^x)*2^x/2=0,-6,5+1,5*2^x+1,5* 2^x=0,2^x=6,5/3,x=log(2)(13/6) +*->x max=-log(2)(13/6)/2+1-log(2)(√13/√2)= log(2)(2√12/13)<0,log(4)(13-3*2^x)≥0,13 3*2^x≥1,2^x≤4,x≤2, xє(-∞;2).
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  5. (2+х)/(2-х)+√х=1+х,{х≥0,2-х≠0;{х≥0,х≠2;х є[0;2)U(2;+∞) 2+x+√x(2-x)=2-x+2x-x²,-(x- 2)√x=-x²,√x(x-2-x¹,⁵)=0,[x=0,(x⁰,⁵)³-(x⁰,⁵)²+ 2=0;(x⁰,⁵-1/3)³-1/3(x⁰,⁵-1/3)+1 25/27=0; x⁰,⁵-1/3=(-26/27+√(26²/27²+(-1/3)³/27)) ^(1/3)+(-26/27-√(676-1)/27)^(1/3)=(-26 +15√3)^(1/3)/3+(-26-15√3)^(1/3)/3= (√3-2)/3+(-√3-2)/3=-4/3,D>0=>1 корень х⁰,⁵=-1,0/{0}
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  6. $sinxdx/(1-cos²x)³=$du/(u²-1)³=$(A/(u-1)+B/(u-1)²+C/(u-1)³+D/(u+1)+E/(u+ 1)²+F/(u+1)³)du=0,5(u-1)^-2/-2-0,5(u+1) ^-2/-2+C=-0,25(cosx-1)^-2+0,25(cosx+1)^-2+C cosx=u,-sinxdx=du 1=A(u-1)²(u+1)³+B(u -1)(u+1)³+C(u+1)³+D(u-1)³(u+1)²+E(u -1)³(u+1)+F(u-1)³=Au⁵+Au⁴-2Au³-2Au²+Au +A+Bu⁴+2Bu³-2Bu-B+Cu³+3Cu²+3Cu+C+Du⁵-Du⁴-2Du³+2Du²+Du-D+Eu⁴-2Eu³+2Eu-E+Fu³-3Fu²+3Fu-F,{A+D=0,A+B-D+E=0,-2 A+2B+C-2D-2E+F=0,-2A+3C+2D-3F=0,A-2B+3C+D+2E+3F=0,A-B+C-D-E-F=1;{A=-D,2A+B+E=0,2B+C-2E+F=0,-4A+3C-3F=0,*2-2B+3C+2E+3F=0,2A-B+C-E-F=1;{A=-D,2A+B+E=0,2B+C-2E+F=0,B+1,5C-1,5F+E=0,-2B+3C+2E+3F=0,2B-C+2E+F=-1;{D=0,A=0,B=0,F=-1/2,E=0,C=1/2;
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  7. (320-(2^-x)²/4)/(128-2^-x)≥2,5 ((2^-x)²/4-2,5*2^-x)/(2^-x-128)≥0,2^-x(2^-x-10)/(2^-x-128)≥0,+°-7-*log(2)10+>x xє(-∞; 7)U[-log(2)10;+∞)
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  8. √ctgx(sin²x-1/4)=0,ctgx≥0,хє(πn;π/2+πn],[x=π/2+πn,sinx=±1/2;[x=π/2+πn,x=±π/6+2πn,x=±5/6π+2πn;[x=π/2+πn,x=π/6+2πn,x=1 1/6π+2πn.
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  9. {c=2-a-b,a=-b/2+1±√(-3/4b²+b); b(b-4/3)≤0 b=0;1 a=1;1;0 c=1;0;1{(1;0;1)(1;1;0)(0;1;1)}
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  10. (х-1)⁵+(х+3)⁵=242(х+1),(х-1+х+3)((х-1)⁴ -(х-1)³(х+3)+..+(х+3)⁴)-242(х+1)=0,2(х+1)((х-1)³(х-1-х-3)-4(х-1)(х+3)+х⁴+4х³*3+4!/2!/2!х²*3²+4х*3³+3⁴-121)=0,[х=-1,-4(х³-3х ²+3х-1)-4х²-12х+4х+12+х⁴+12х³+54х²+108х-40=0,-4х³+12х²-12х+4+х⁴+12х³+50х²+100х-28=0,х⁴+8х³+62х²+88х-24=0,(х²+4х +23)²-96х-553=0,240=240,х=-2,х³+6х²+50х-12=0,(х+2)³+38(х+2)-96=0,х+2=(48+2 √(87810)/9)^(1/3)+(48-2√(87810)/9)^ (1/3),х=-2+(48+2√(87810)/9)^(1/3)+(48 -2√(87810)/9)^(1/3){-2;-1;-2+(48+2√(8 7810)/9)^(1/3)+(48 -2√(87810)/9)^(1/3)}
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