Problem

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Tags: inequalities, search, inequalities proposed



$a,b,c$ are positive real numbers. prove the following inequality: $\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}+\frac{1}{(a+b+c)^2}\ge \frac{7}{25}(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}+\frac{1}{a+b+c})^2$ (20 points)