[tex]\left \{ \left. a;b;c \right \} \right.=\left \{ \left. \frac{1}{x};\frac{1}{y};\frac{1}{z} \right \} \right.\rightarrow xyz=1[/tex]
[tex]M=\sum \frac{bc}{a^2(b+c)}=\sum \frac{\frac{1}{yz}}{\frac{1}{x^2}(\frac{1}{y}+\frac{1}{z})}=\sum \frac{x^2}{yz(\frac{1}{y}+\frac{1}{z})}=\sum \frac{x^2}{y+z}\geq \frac{(x+y+z)^2}{2(x+y+z)}=\frac{x+y+z}{2}\geq \frac{3\sqrt[3]{xyz}}{2}=\frac{3}{2}[/tex]