Question

Реши уравнение:
2x(x−9)^2−x^2(x−9)=0

Answer 1

$2x(x-9)^2-x^2(x-9)=0 \ 2x(x^2-18x+81)-x^3+9x^2=0 \ 2x^3-36x^2+162x-x^3+9x^2=0 \ x^3-27x^2+162x=0 \ x(x^2-27x+162)=0 \ x^2-27x+162=0 \ D=729-648=81 \ x_{1,2} = frac{27 pm 9}{2} = left { {{x_1=9} atop {x_2=18}} right. \ \ x_1 = 9 ; x_2 = 18 ; x_3=0$