# Minimum again?

Algebra Level 5

$\large\left(a+\dfrac{1}{a}\right)^9 +\left(b+\dfrac{1}{b}\right)^9+\left(c+\dfrac{1}{c}\right)^9$

If $a,b$ and $c$ are positive real numbers such that their sum is 1, find the minimum value of the expression above.

If the minimum value can be expressed as $\dfrac{ w^x}{y^z}$ for positive integers $w,x,y$ and $z$, submit your answer as $w+x+y+z$.

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