Question

Решите уравнение
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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:
$\ x_{1,2} = - 3±2 sqrt{2}\x_{3} =0\x_{4} =-6$