8. Solve the equation $x^{7} \cdot \sqrt{2+x-x^{2}}+(2-x)^{11} \cdot \sqrt{3 x-x^{2}}=0$.
Answer: $x=0, x=2$

Solution: The domain of this equation is the interval [0;2]. On this interval, both terms are non-negative. Their sum is zero only when both are zero. The first term is zero at $x=-1,0,2$, and the second term is zero at $x=0,2,3$. Only 0 and 2 coincide.

## Variant 2-b