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 \(P = \dfrac{a^2}{b + 2c} +\dfrac{b^2}{c + 2a}+ \dfrac{c^2}{a + 2b}.\)