[1, 2]

danghajdang

With $ a_{1}, a_{2}, ..., a_{9}, b_{1}, b_{2},..., b_{9} \in [1, 2]$ and:
$ a_{1}^{2}+ a_{2}^{2}+ ...+ a_{9}^{2}= b_{1}^{2}+ b_{2}^{2}+ ...+ b_{9}^{2}$
Prove that:
$ \sum_{m= 1}^{9}\frac{a_{m}^{3}}{b_{m}}\leq  \frac{5}{3}\sum_{m= 1}^{9}a_{m}^{2}$