Question

Решить уравнение, заменив х^2+3х на а.

Answer 1

$\sqrt{x^2 + 3x + 12} - \sqrt{x^2 + 3x} = 2 \\ a = x^2 + 3x \\ \sqrt{a + 12} - \sqrt{a} = 2 |^2 \\ 2a + 12 - 2\sqrt{a^2 + 12a} = 4 \\ a + 4 = \sqrt{a^2 + 12a} \\ a^2 + 8a + 16 = a^2 + 12a \\ 4a = 16 \\ a = 4 \rightarrow x^2 + 3x - 4= 0 \rightarrow (x + 4)(x - 1) = 0 \\ x_1 = 1 \\ x_2 = -4$