Question

найдите корни уравнений​

Answer 1

$7(x+frac{1}{x})-2(x^2+frac{1}{x^2})=9 : : : : : | : xne0\7x+frac{7}{x}-2x^2-frac{2}{x^2}=9\7x+frac{7}{x}-2x^2-frac{2}{x^2}-9=0\frac{7x^3+7x-2x^4-2-9x^2}{x^2}=0\7x^3+7x-2x^4-2-9x^2=0\-2x^4+7x^3-9x^2+7x-2=0\-2x^4+x^3+6x^3-3x^2-6x^+3x+4x-2=0\-x^3(2x-1)+3x^2(2x-1)-3x(2x-1)+2(2x-1)=0\-(2x-1)(x^3-3x^2+3x-2)=0\-(2x-1)((x-1)^3-1)=0\(2x-1)((x-1)^3-1)=0\2x-1=0\2x=1\x=frac{1}{2}\x_1=0,5\(x-1)^3-1=0\x_2=2$