|x^2-x-1|=x^2+2x+1 помогите

Question

|x^2-x-1|=x^2+2x+1
помогите

Answer 1

Правая часть = x^2 + 2x +1 = (x+1)^2 >=0;
x^2 - x - 1 = x^2 + 2x + 1; или x^2 - x - 1 = -(x^2 + 2x +1).
1) x^2 - x-1 = x^2 +2x+1;
2x+x = -1-1;
x1 = -2/3.
2) x^2 - x - 1 = -x2 - 2x -1;
2*(x^2) - x +2x = 0;
2*(x^2) + x = 0;
x*( 2x+1) = 0;
x2 = 0
или 2x+1 = 0; <=> x3 = -1/2
Ответ. { -2/3; -1/2; 0}.