Đáp án:
`x=9/4`
Giải thích các bước giải:
`A=(\frac{2}{\sqrt[x]+3}-1/\sqrt[x]):\frac{\sqrt[x]-2}{x+3\sqrt[x]}`
`A=\frac{2\sqrt[x]-\sqrt[x]-3}{\sqrt[x].\sqrt[x]+3}.\frac{x+3\sqrt[x]}{\sqrt[x]-2}`
`A=\frac{\sqrt[x]-3}{\sqrt[x].(\sqrt[x]+3)}.\frac{\sqrt[x](\sqrt[x]+3)}{\sqrt[x]-2}`
`A=\frac{\sqrt[x]-3}{\sqrt[x]-2}`
Để `A=3` `⇔ \frac{\sqrt[x]-3}{\sqrt[x]-2}=3` $(x\neq4)$
`⇒` `\sqrt[x]-3=3(\sqrt[x]-2)`
`⇔` `\sqrt[x]-3=3\sqrt[x]-6`
`⇔` `2\sqrt[x]=3`
`⇔` `\sqrt[x]=3/2`
`⇔` `x=(3/2)^2=9/4` $(\text{thỏa mãn})$
Vậy `x=9/4` thì `A=3`
