Решите уравнение : [latex] \sqrt{(x+1)(2x+3)} =x+3 ;[/latex]

[latex]\sqrt{(x+1)(2x+3)} = x+3[/latex] ОДЗ: [latex]x + 3 \geq 0, \ x \geq -3\\\\ (x+1)(2x+3) \geq 0, \ x \in (-\infty;-\frac{3}{2}] \cup [-1;+\infty)[/latex] [latex](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}[/latex]