# A number theory problem by abhishek anand

Let $$x_1$$, $$x_2$$, $$\dots$$, $$x_{2014}$$ be real numbers different from 1, such that $$x_1 + x_2 + \dots + x_{2014} = 1$$ and $\frac{x_1}{1 - x_1} + \frac{x_2}{1 - x_2} + \dots + \frac{x_{2014}}{1 - x_{2014}} = 1.$ Find the value of $\frac{x_1^2}{1 - x_1} + \frac{x_2^2}{1 - x_2} + \dots + \frac{x_{2014}^2}{1 - x_{2014}}.$

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