Minimize $P=5\left(x^2+y^2\right)+2z^2$ For $\left(x+y\right)\left(x+z\right)\left(y+z\right)=144$, minimize $$P=5\left(x^2+y^2\right)+2z^2$$
I have no idea. Can you make a few suggestions? 

HINT: prove that $$P=5(x^2+y^2)+2z^2\geq 72$$ and the equal sign will atained at $$(x,y,z)=(2,2,4)$$
