Question

Решите уравнение:
х(х^2 - 6х + 5) = 12(х - 5)

Answer 1

$x^2-6x+5=0 \\ D=36-4*5*1=16 \\ x_{1,2} = 6+/-4/2 \\ x_1 = 5 ; x_2 = 1 \\ x(x-5)(x-1)=12(x-5) \\ x=5 x(x-5)(x-1)-12(x-5)=0 \\ x^3-6x^2-7x+60=0 \\ (x^3-6x^2-7x+60)/(x-5) = \\ x^2-x-12 \\ D=1-4*(-12)*1=49 \\ x_{1,2} = 1+/-7/2 \\ x_1 = 4 ; x_2 = -3 \\ x_1 = 5 ; x_2 = 4 ; x_3 = -3$