gt$\Rightarrow$$\frac{1}{x}$+$\frac{1}{y}$+$\frac{1}{z}$=1Áp dụng BĐT:$\sum_{i=1}^{n}$$\frac{1}{ai}$$\geq$$\frac{n^{2}}{\sum_{i=1}^{n}ai }$
$\Rightarrow$$\frac{1}{4x+3y+z}$$\leq$$\frac{1}{64}$($\frac{4}{x}$+$\frac{3}{y}$+$\frac{1}{z}$)
Tương tự$\Rightarrow$M$\leq$$\frac{1}{64}$($\frac{8}{x}$+$\frac{8}{y}$+$\frac{8}{z}$)=$\frac{1}{8}$
Dấu''='' xra$\Leftrightarrow$x=y=z=3