Question

(х²+2х)²-2(х²+2х)-3=0. срооочнооооо

Answer 1

$(x^2+2x)^2-2(x^2+2x)-3=0\\\\x^2+2x=t\\\\t^2-2t-3=0\\\\D_t=(-2)^2-4\cdot1\cdot(-3)=4+12=16\\\\\sqrt{D_t}=\sqrt{16}=4\\\\t_1=\frac{2-4}{2\cdot1}=\frac{-2}{2}=-1\\\\t_2=\frac{2+4}{2\cdot1}=\frac{6}{2}=3$

$x^2+2x=-1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x^2+2x=3\\\\x^2+2x+1=0\ \ \ \ \ \ \ \ \ \ \ \ \ \ x^2+2x-3=0\\\\(x+1)^2=0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x^2+3x-x-3=0\\\\x+1=0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x(x+3)-(x+3)=0\\\\x=-1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (x+3)(x-1)=0\\\\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x=-3\ \ \ \ \ \ x=1$

Ответ: -  3; - 1; 1