# Another Max-min problem!

Algebra Level pending

Given two positive real numbers $$x,y$$ that satisfy: $$x \ge 1, y \ge 1, 3(x+y)=4xy$$.

Let $$P=x^3+y^3+3\left(\displaystyle\frac{1}{x^2}+\displaystyle\frac{1}{y^2}\right)$$

If $$\max {P} + \min {P} = \displaystyle\frac{a}{b}$$, where a and b are coprime positive integers, find $$a+b$$.

This problem is not original.

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