jmc

Let $x_1,$ $x_2,$ $\dots ,$ $x_{100}$ be real numbers such that $x_1+x_2+\cdots +x_{100}=1$ and $$\frac{x_1}{1-x_1}+\frac{x_2}{1-x_2}+\cdots +\frac{x_{100}}{1-x_{100}}=1.$$Find $$\frac{x_1^2}{1-x_1}+\frac{x_2^2}{1-x_2}+\cdots +\frac{x_{100}^2}{1-x_{100}}.$$