16. Suppose $x$ and $y$ are two real numbers such that $x+y=10$ and $x^{2}+y^{2}=167$. Find the value of $x^{3}+y^{3}$.
16 Ans: 2005.
$$
167=(x+y)^{2}-2 x y \Longrightarrow x y=-\frac{67}{2} \text {. Hence } x^{3}+y^{3}=(x+y)\left(x^{2}-x y+y^{2}\right)=2005 \text {. }
$$