AM GM only?

Algebra Level 2

Let a,b,ca,b,c be three real positive numbers and a2+b2+c2=3a^2+b^2+c^2=3. Find the minimum of the expression P=a2b+2c+b2c+2a+c2a+2b.P = \dfrac{a^2}{b + 2c} +\dfrac{b^2}{c + 2a}+ \dfrac{c^2}{a + 2b}.

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