For classical inequalities lovers

Algebra Level 4

Let a,ba, b and cc positive real numbers such that 1a2+1b2+1c2=9\dfrac{1}{a^2} +\dfrac{1}{b^2} +\dfrac{1}{c^2}=9. If MM is the maximum value of the following expression 12a+b+12b+c+12c+a, \frac{1}{2a+b} +\frac{1}{2b+c} +\frac{1}{2c+a}, enter M2M^2 as your answer.

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