6.155. $a x^{4}-x^{3}+a^{2} x-a=0$.

6.155. $a x^{4}-x^{3}+a^{2} x-a=0$.
## Solution.

We have $\left(a x^{4}-x^{3}\right)+\left(a^{2} x-a\right)=0 \Leftrightarrow x^{3}(a x-1)+a(a x-1)=0 \Leftrightarrow$ $\Leftrightarrow(a x-1)\left(x^{3}+a\right)=0$. Then $a x-1=0$, from which $x_{1}=\frac{1}{a}$, or $x^{3}+a=0$, from which $x_{3}=\sqrt[3]{-a}=-\sqrt[3]{a}$ when $a \neq 0 ; x=0$ when $a=0$.

Answer: $x_{1}=\frac{1}{a}, x_{2}=-\sqrt[3]{a}$ when $a \neq 0 ; x=0$ when $a=0$.