16. Suppose that $x_{1}$ and $x_{2}$ are the two roots of the equation $(x-2)^{2}=3(x+5)$. What is the value of the expression $x_{1} x_{2}+x_{1}^{2}+x_{2}^{2}$ ?
16. Answer: 60
The equation $(x-2)^{2}=3(x+5)$ is equivalent to $x^{2}-7 x-11=0$. Thus $x_{1}+x_{2}=7$ and $x_{1} x_{2}=-11$. So
$$
x_{1} x_{2}+x_{1}^{2}+x_{2}^{2}=\left(x_{1}+x_{2}\right)^{2}-x_{1} x_{2}=7^{2}-(-11)=60 .
$$