`#tnvt`
`C=\frac{x}{\sqrt{x}-2}(x>4)`
`=\frac{x-4+4}{\sqrt{x}-2}`
`=\frac{(\sqrt{x}-2)(\sqrt{x}+2)+4}{\sqrt{x}-2}`
`=\sqrt{x}+2+\frac{4}{\sqrt{x}-2}`
`=\sqrt{x}-2+\frac{4}{\sqrt{x}-2}+4`
Áp dụng BĐT Cauchy cho hai số dương, ta có:
`(\sqrt{x}-2)+\frac{4}{\sqrt{x}-2}>=2\sqrt{(\sqrt{x}-2).\frac{4}{\sqrt{x}-2}}=2\sqrt{4}=4`
Dấu `=` xảy ra khi `\sqrt{x}-2=\frac{4}{\sqrt{x}-2}`
`<=>(\sqrt{x}-2)^2=4`
`<=>\sqrt{x}-2=2(x>4)`
`<=>\sqrt{x}=4`
`<=>x=16(tm)`
Vậy `GTNNNN=4` khi `x=16`
