Question

$x^{4}+ x^{3}-4x ^{2}-2x+4=0$ Плз решение

Answer 1

$x^4+x^3-4x^2-2x+4=0 \ (x^4+4)+x(x^2-2)-4x^2=0 \ (x^4-4x^2+4+4x^2)+x(x^2-2)-4x^2=0 \ (x^2-2)^2+4x^2+x(x^2-2)-4x^2=0 \ (x^2-2)^2+x(x^2-2)=0 \ frac{(x^2-2)^2}{x^2} + frac{x^2-2}{x} =0 \ t= frac{(x^2-2)}{x} \ t(t+1)=0 \ t=-1, t=0 \ frac{x^2-2}{x} =-1 frac{x^2-2}{x} =0 \ 1) frac{x^2-2}{x} +1=0 \ x^2+x-2=0 \ x=-2, x=1 \ 2)x^2-2=0, x^2=2 \ x=- sqrt{2} ,x= sqrt{2} \ Ответ: x=-2, x=- sqrt{2} , x=1, x= sqrt{2}$