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

  1. √(x³+17)=3x-5+√(x³+8),{x³+17=(3x-5)² +2(3x-5)√(x³+8)+x³+8,3x-5+√(x³+8)≥0;{(6x-10)√(x³+8)=-9x²+30x-16,√(x³+8)≥-3x+5;{36x⁵-201x⁴+640x³-900x²+544=0,(x-2/3)(х-8/3)/(х-5/3)≤0-*2/3+*5/3-*8/3 +>х; [{x≥3+(-9/2+√85/2)^(1/3)+(-4,5-√85/ 2)^(1/3), x≤5/3;x>5/3; 0,425✓{[х=1,26.., х=2,х=-0,625..,хє(-∞;2/3]U(5/3;8/ 3];хє[3+(-9/2+√85 /2)^(1/3)+(-4,5-√85/2)^ (1/3);∞);{[х=2,0/,0/,хє(5/3;8/3];{2}
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  2. tga=10/h,tg(45°-a)=3/h,1=(10/h+3/h)/(1-10/h*3/h),1-30/h²=13/h,-30(1/h)²-13/h+1=0 1/h=(13±√(13²-4*30))/-60[1/h= 0,5 1/h=1/15;h=15 arctg7,5 BD=tg(arctg7,5-45°)*3=(7,5-1)/(1+7,5*1)*3=6,5/8,5*3=39/17
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  3. AB/sin70°=BD/sin30°=AD/sin80° AC=AB +0,5AB/sin70° (AB+0,5/sin70AB)/sin70°= AB/sinx,x=(-1)^narcsin(cos²20°/4/(cos1 0°-0,5)/(cos10°+0,5))+πn x=arcsin(cos ²20°/4/(cos10°-0,5)/(cos10°+0,5))
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  4. x^(1/x)=(y^(1/y))²≤e^(1/e) e^(2lny/y)(2/y²-2lny/y2)=0 y=e+*->y 2^(1/4)=16^(1/16) (2;16)(-2;-16) 4^(1/8)=16^(1/16)(4;16)(-4;-16)
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  5. S∆,S∆/4 S∆/6 5S∆/12=5 S∆=12
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  6. 0≥√(2x-3)*log|cosx|((1+2√3|sinx|)/8/- cos2x) x+1,5 16|sinx|²-2√3|sinx|-9=0 |sinx|=(√3±7√3)/16=√3/2;-3√3/8≥0 sinx=± √3/2 x=±π/3+2πn;±2/3π+2πn x=±π/3+πn *1,5°0,5π+*2/3π°π*1 1/3π+°1,5π>x x{1,5}U{2/3π+πn}U{1 1/3π+πn}
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  7. y''/y'=yy'/(y²-1) ln|Y'|=ln|y²-1|/2+c y'=|y²-1|⁰,⁵c y'/(y²-1)⁰,⁵=c ln|y+(y²-1)⁰,⁵|=cx+c1 0,5e^(-cx)/c1+0,5e^(cx)c1=y
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  8. lnx=0;±5¹/⁴ x=1;e^(±5¹/⁴) x=e^(±100¹/⁴/2)(cos(100⁰,²⁵/2)±isin(100 ⁰,²⁵/2))
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  9. х=(-1/2+√(1/4+2021³/27))^(1/3)+(-1/2+√(1/4+2021³/27))^(1/3)=(-0,5+√33'018'621'021'071/6/√3)^(1/3)+(-0,5-√33'018'621'021'071/6/√3)^(1/3) 2021 2021 2021 4042 4042 4084441 *2021 4084441 8168882 8168882 8'254'655'261*4=33'018'621'044+27=33'018'621'021'071
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  10. 3xf-4x=2f-20 f=(4x-20)/(3x-2) f(5)=0
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  11. log(72)√18=log(72)n n=√18
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  12. 1/1!-1/2!+1/2!-1/3!..+1/k!-1/(k+1)!=1-1/(k +1)! 2019(1-(1-1/(2019)!))=1/2018!
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  13. R,2a-R,(2a-R)²+a²=R²,4a²-4aR+R²+a²-R²= 0,R=5/4a 5/4a=5,a=4 S=32
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  14. f(x+f(y))=x+y+1,x=0,f(f(y))=y+1,f(y)=ky+b,f(f(y))=k(ky+b)+b=k²y+kb+b²=y+1,{k²=1,kb+b²=1;[{k=1,b²+b-1=0;{k=-1,b²-b-1 =0;[{k=1,b=(-1±√(1-4*-1))/2;{k=-1,b=(1±√ 5)/2;f(x)=x-0,5±√5/2,f(x)=-x+0,5±√5/2,
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  15. f(x+y)=fx+fy-xy,f(y)=f0+fy,f0=0 f(2x)=2fx -x²,f(2^(n+1))=2^(n+1)f1-2^(2n+1)+2^n,f(x)=2xf1-x²/2+0,5x,f1=2f1,f1=0 fx=-x²/2+0,5 x
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  16. 1771/69=25 345=460-
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  17. log(x+1)=logx+1,{x+1=x*10,x+1>0;{x=1/9, x>-1;{1/9}
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  18. y=x^a^a+a^x^a+
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