`ĐKXĐ: x>=0`
`A=(x+8)/(\sqrt{x}+1)`
`A=(x-1+9)/(\sqrt{x}+1)`
`A=(x-1)/(\sqrt{x}+1)+9/(\sqrt{x}+1)`
`A=((\sqrt{x}+1)(\sqrt{x}-1))/(\sqrt{x}+1)+9/(\sqrt{x}+1)`
`A=\sqrt{x}-1+9/(\sqrt{x}+1)`
`A=\sqrt{x}+1+9/(\sqrt{x}+1)-2`
Áp dụng bất đẳng thức `Cosi` ta có:
`A>=2\sqrt{(\sqrt{x}+1).(9)/(\sqrt{x}+1)}-2=2\sqrt{9}-2=2.3-2=6-2=4`
Dấu `=` xảy ra
`<=>\sqrt{x}+1=9/(\sqrt{x}+1)`
`<=>(\sqrt{x}+1)^2=9`
`<=>\sqrt{x}+1=+-3`
`<=>[(\sqrt{x}+1=3),(\sqrt{x}+1=-3):}`
`<=>[(\sqrt{x}=2),(\sqrt{x}=-4(\text{VÔ LÍ})):}`
`<=>x=4(TM)`
Vậy `minA=4` khi `x=4`
