Question

(x²- x+1) (x²-x+7) =65​

Answer 1

(x² - x + 1)(x² - x - 7) = 65

Сделаем замену :

x² - x + 1 = m , тогда  x² - x - 7 = m - 8

m(m - 8) = 65

m² - 8m - 65 = 0

D = (- 8)² - 4 * (- 65) = 64 + 260 = 324 = 18²

$m_{1} =frac{8-18}{2}=-5\\m_{2}=frac{8+18}{2}=13\\1)x^{2}-x+1=-5\\x^{2}-x+6=0\\D=(-1)^{2} -4*6=1-24=-23<0\\2)x^{2}-x+1=13\\x^{2}-x-12=0\\x_{1}=-3\\x_{2}=4\\Otvet:boxed{-3;4}$