# AM GM only?

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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