So which one is it?

Algebra Level 4

aba2+3b2+cbb2+3c2+acc2+3a2\frac{ab}{a^{2}+3b^{2}}+\frac{cb}{b^{2}+3c^{2}}+\frac{ac}{c^{2}+3a^{2}}

If the maximum value of the above inequality is MM for positive numbers a,b,ca,b,c. What is the value of 4M+44M + 4 ?

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