$\displaystyle P=(5a+\frac{2}{b+c})^{3}+(5b+\frac{2}{c+a})^{3}+ (5c+\frac{2}{a+b})^{3}$
where $\displaystyle a,b,c$ are positive real numbers satisfying: $\displaystyle a^{2}+b^{2}+c^{2}=3$