Question

Найдите произведение корней уравнения (x^2-9)^2-27(x^2-9)-520=0

Answer 1

$\displaystyle (x^2-9)^2-27(x^2-9)-520=0\\\\x^2-9=t\\\\t^2-27t-520=0\\\\D=729+2080=2809=53^2\\\\t_1=(27+53)/2=40\\\\t_2=(27-53)/2=-13\\\\x^2-9=40; x^2=49; x=\pm 7\\\\x^2-9=-13; x^2=-4; x\in O$

ответ  х=7 или х=-7

Тогда х1*х2= -49