Question

Реши уравнение:
2x(x−9)^2−x^2(x−9)=0

Answer 1

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