Question

решите уравнение x (x-2)(x+1)=(x^2-1)*x^2



дам 40 баллов

Answer 1

Ответ:

$x(x - 2)(x + 1) = ( {x}^{2} - 1) {x}^{2} \\ x(x - 2)(x + 1) = (x - 1)(x + 1) {x}^{2} \\ x(x - 2)(x + 1) - (x - 1)(x + 1) {x}^{2} = 0 \\ (x + 1)(x(x - 2) - (x - 1) {x}^{2} ) = 0 \\ 1) \: \: \: x + 1 = 0 \\ x1 = - 1 \\ \\ x(x - 2) - (x - 1) {x}^{2} = 0 \\ x(x - 2 - (x - 1)x) = 0 \\ 2) \: \: \: x2 = 0 \\ \\ x - 2 - {x}^{2} + x = 0 \\ - {x}^{2} + 2x - 2 = 0 \\ {x}^{2} - 2x + 2 = 0 \\ d = 4 - 8 = - 4 \\ d < 0$

d<0 значит корней нет

ответ: -1, 0;