# Thread: Find min

1. ## Find min

Find the minimum value of the expression:
$P=(5a+\frac{2}{b+c})^{3}+(5b+\frac{2}{c+a})^{3}+ (5c+\frac{2}{a+b})^{3}$
where $a,b,c$ are positive real numbers satisfying: $a^{2}+b^{2}+c^{2}=3$

2. Please post your thoughts or attempted solution.