Question

Решите уравнение:

x^3*(^2 − 6 + 9) − 4(^2 − 6 + 9) = 0.

Answer 1

$\displaystyle\bf\\x^{3} \cdot(x^{2} -6x+9)-4x\cdot(x^{2} -6x+9)=0\\\\x^{3} \cdot(x-3)^{2} -4x\cdot(x-3)^{2} =0\\\\(x-3)^{2} \cdot(x^{3} -4x)=0\\\\x\cdot(x^{2} -4)\cdot(x-3)^{2} =0\\\\x\cdot(x-2)\cdot(x+2)\cdot(x-3)^{2} =0\\\\x_{1} =0\\\\x-2=0 \ \ \ \Rightarrow \ \ \ x_{2} =2\\\\x+2=0 \ \ \ \Rightarrow \ \ \ x_{3} =-2\\\\x-3=0 \ \ \ \Rightarrow \ \ \ x_{4} =3\\\\Otvet \ : \ 0 \ \ ; \ \ 2 \ \ ; \ \ -2 \ \ ; \ \ 3$