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Algebra Level 2

Let $a,b,c$ be three real positive numbers and $a^2+b^2+c^2=3$ . Find the minimum of the expression $P = \dfrac{a^2}{b + 2c} +\dfrac{b^2}{c + 2a}+ \dfrac{c^2}{a + 2b}.$

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by Mardokay Mosazghi

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