Question

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

Answer 1

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