Question

Решить уравнение
x^2+2x+3*√(x^2+2x-2)=6

Answer 1

$x^{2} + 2x + 3\sqrt{x^{2} + 2x - 2} = 6$

$\displaystyle x^{2} + 2x \underbrace{- 2 + 2}_{0} + 3\sqrt{x^{2} + 2x - 2} = 6$

Замена: $\sqrt{x^{2} + 2x - 2} = t \geq 0$

$t^{2} + 2 + 3t = 6$

$t^{2} + 3t - 4 = 0$

$t_{1} = -4 < 0; \ t_{2} = 1$

$t = 1$

Обратная замена:

$\sqrt{x^{2} + 2x - 2} = 1$

$x^{2} + 2x - 2 = 1$

$x^{2} + 2x - 3 = 0$

$x_{1} = -3; \ x_{2} = 1$

ответ: $x_{1} = -3; \ x_{2} = 1$