Question

Решите уравнение : 
$sqrt{(x+1)(2x+3)} =x+3 ;$

Answer 1

$sqrt{(x+1)(2x+3)} = x+3$

ОДЗ:

$x + 3 geq 0, x geq -3\\ (x+1)(2x+3) geq 0, x in (-infty;-frac{3}{2}] cup [-1;+infty)$


$(x+1)(2x+3) = (x + 3)^2\\ 2x^2 + 5x + 3 = x^2 + 6x + 9\\ x^2 - x - 6 = 0\\ x^2 - 3x + 2x - 6 = 0\\ x(x - 3) + 2(x - 3) = 0\\ (x + 2)(x - 3) = 0\\ boxed{mathbb{OTBET}: x_1 = -2, x_2 = 3}$