Решите уравнения, разложив на множители.

1) x (x^2-x-6) = x^2-9;

2) x^2-25 = (x-1) (x^2-2x-35) ;

1) x (x^2-x-6) = x^2-9

x²-x-6=0

x1+x2=1 U x1*x2=-6⇒x1=-2 U x2=3

x (x+2) (x-3) - (x-3) (x+3) = 0

(x-3) (x²+2x-x-3) = 0

(x-3) (x²+x-3) = 0

x-3=0⇒x=3

x²+x-3=0

D=1+12=13

x = (-1-√13) / 2 U x = (-1+√13) / 2

Ответ x={3; (-1-√13) / 2; (-1+√13) 2}

2) x^2-25 = (x-1) (x^2-2x-35)

x²-2x-35=0

x1+x2=2 U x1*x2=-35⇒x1=-5 U x2=7

(x-5) (x+5) - (x-1) (x+5) (x-7) = 0

(x-5) (x+5-x²+7x+x-7) = 0

(x-5) (x²-9x+2) = 0

x-5=0⇒x=5

x²-9x+2=0

D=81-8=73

x = (9-√73) / 2 U x = (9+√73) / 2

Ответ x={5; (9-√73) / 2; (9+√73) / 2}