5. Solve the equation $(\sqrt{x})^{2016}+(\sqrt{1-x})^{2016}=1$

ANSWER: $x=0$ or 1.
Solution: From the domain of definition $0<=x<=1$. It is clear that 0 and 1 are valid. If $0<x<1$, then $(\sqrt{x})^{2016}+(\sqrt{1-x})^{2016}<x+(1-x)=1$, and cannot be a solution.