A number theory problem by abhishek anand

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


The answer is 0.

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1 solution

An easy cute one Abhishek. let the sum given be s1 and s2 respectively.s2-s1 gives you the answer.

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