<s>[INST] Find the Minimum value of this expression Let $x,y,z>0$ such that: $x+y+z=1$. Find the minimum value of this expression.
$P=(\frac{x+1}{x})^3.\frac{z^2}{z^2+1}+(\frac{y+1}{y})^3.\frac{x^2}{x^2+1}+(\frac{z+1}{z})^3.\frac{y^2}{y^2+1}$
 [/INST] Hint : 
use Lagrange multipliers 
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