Cách khác:
$M=\frac{y\sqrt{x-1}+x\sqrt{y-4}}{xy}$
$=\frac{\sqrt{x-1}}{x}+\frac{\sqrt{y-4}}{y}$
$=\frac{2\sqrt{(x-1).1}}{2x}+\frac{2\sqrt{(y-4).4}}{4y}\leq \frac{x-1+1}{2x}+\frac{y-4+4}{4y}$ (BĐT Cauchy)
$=\frac{1}{2}+\frac{1}{4}=\frac{3}{4}$
Dấu "=" xảy ra <=> x=2;y=8