Question

Решите уравнение / - дробь 1/x^2+6x+5 + 18/x^2+6x+10 = 18/x^2+6x+9

Answer 1

$\frac{1}{ {x}^{2} + 6x + 5 } + \frac{18}{{x}^{2} + 6x +10} = \\ = \frac{18}{{x}^{2} + 6x +9} \\ y = {x}^{2} + 6x + 9 \\ \frac{1}{y - 4} + \frac{18}{y + 1} = \frac{18}{y} \\ \frac{1}{y - 4} = \frac{18}{y } - \frac{18}{y + 1} \\ \frac{1}{y - 4} = \frac{18}{y(y + 1)} \\ 18(y - 4) = {y + y}^{2} \\ {y}^{2} - 17y + 72 = 0 \\ (y - 8)(y - 9) = 0 \\ y_1 = 8 \\ y_2 = 9 \\ (x + 3) ^{2} = 8 \\ x + 3 = ±2 \sqrt{2} \\ x_{1,2} = - 3±2 \sqrt{2} \\ (x + 3) ^{2} = 9\\ x + 3 = ±3 \\x_{3} =0\\x_{4} =-6$
Ответ:
$\\\\ x_{1,2} = - 3±2 \sqrt{2}\\x_{3} =0\\x_{4} =-6$