# An algebra problem by Priyanshu Mishra

Algebra Level 5

If $$(x,y,z)$$ are non-negative reals and $$xy + yz + zx = 1$$,

The maximum value of the expression below is of the form $$\large \frac { a }{ b\sqrt { c } }$$.

$$\large\ x\left( 1-{ y }^{ 2 } \right) \left( 1-{ z }^{ 2 } \right) + y\left( 1-{ z }^{ 2 } \right) \left( 1-{ x }^{ 2 } \right) + z\left( 1-{ x }^{ 2 } \right) \left( 1-{ y }^{ 2 } \right)$$

$$a,b,c$$ are all positive integers with $$a,b$$ coprime and $$c$$ square-free.

Find $$a + b + c$$.

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