đề đúng là phải
$P=\frac{4x+y}{xy}+\frac{2x-y}{4}$
$<=> P=\frac{4}{y}+\frac{1}{x}+\frac{x}{2} - \frac{y}{4}$
$=>P=\frac{4}{y}+\frac{1}{x}+\frac{x}{2}-\frac{5-x}{4}$ (thay $y=5-x$)
$<=> P=\frac{4}{y} + \frac{1}{x} + \frac{3x}{4} -\frac{5}{4} (*)$
Áp dụng BĐT Cauchy ta có:
$\frac{4}{y}+\frac{y}{4} \geq2 ("=" khi y=4)$
$\frac{1}{x}+x \geq 2$ $"=" khi x= 1$
$=> \frac{4}{y}+\frac{y}{4} +\frac{1}{x}+x \geq4$
<=>$\frac{4}{y} +\frac{1}{x} +\frac{3x}{4} -\frac{5}{4} \geq4- \frac{x+y}{4} -\frac{5}{4}$
$<=> P \geq\frac{3}{2}$ ( thay $ x+y =5 )$
Vậy $Pmin =\frac{3}{2} khi x=1 ; y=4 $
Đúng thì vote ~~ sai thì sửa :D