Question

Решите уравнение пожалуйста

Answer 1

(x² - 5x)² - 30x(x - 5) - 216 = 0

[x(x - 5)]² - 30[x(x - 5)] - 216 = 0

Сделаем замену :

x(x - 5) = m

m² - 30m - 216 = 0

D = (- 30)² - 4 * (- 216) = 900 + 864 = 1764 = 42²

$m_{1}=\frac{30-42}{2}=-6\\\\m_{2}=\frac{30+42}{2}=36\\\\1)x(x-5)=-6\\\\x^{2}-5x+6=0\\\\x_{1}=2\\\\x_{2}=3-teorema-Vieta\\\\2)x(x-5)=36\\\\x^{2}-5x-36=0\\\\x_{3}=-4\\\\x_{4} =9\\\\Otvet:\boxed{2;3;-4;9}$