Solve the equation $\left(x^{2}-x+1\right)^{4}-10 x^{2}\left(x^{2}-x+1\right)^{2}+9 x^{4}=0$.
Let $y=\left(x^{2}-x+1\right)^{2}$, then $y^{2}-10 x^{2} y+9 x^{4}=0$. Solving this equation for $y$, we get: $y_{1}=9 x^{2}, y_{2}=$ $x^{2}$.

Thus, the given equation has been reduced to the following two: $\left(x^{2}-x+1\right)^{2}=9 x^{2}$ and $\left(x^{2}-x+1\right)^{2}=x^{2}$, which in turn lead to four quadratic equations:

$x^{2}-x+1=3 x, x^{2}-x+1=-3 x, x^{2}-x+1=x, x^{2}-x+1=-x$.

## Answer

$-1,1,2-\sqrt{3}, 2+\sqrt{3}$