# A.M-G.M Inequality

Algebra Level 4

Let $$a,b$$ and $$c$$ be positive numbers satisfying $$a+b+c=3$$. If the maximum value of $$a^2 b^3 c^2$$ can be expressed as $$3^p \times 2^q \times 7^r$$, where $$p,q,r$$ are integers, find the value of $$p+q+r$$.

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