[Toán 9] $2(x\sqrt{y-4}+y\sqrt{x-4})=xy$

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hthtb22

Bài làm
Pt \Leftrightarrow $$\frac{\sqrt{y-4}}{y}+\frac{\sqrt{x-4}}{x}=\frac{1}{2}$$

Áp dụng bđt Cauchy ta có:

$\frac{\sqrt{y-4}}{y}=\frac{\sqrt{4(y-4)}}{2y}$ \leq $\frac{4+(y-4)}{2.2y}=\frac{1}{4}$
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