Đáp án:
Giải thích các bước giải:
a) Xét `M=(2x+1)/(\sqrt{x^3}-1) - \sqrt{x}/(x+\sqrt{x}+1)`
`=(2x+1)/(\sqrt{x}^3-1) - \sqrt{x}/(x+\sqrt{x}+1)`
`=(2x+1-\sqrt{x}(\sqrt{x}-1))/((\sqrt{x}-1)(x+\sqrt{x}+1))`
`=(2x+1-x+\sqrt{x})/((\sqrt{x}-1)(x+\sqrt{x}+1))`
`=(x+\sqrt{x}+1)/((\sqrt{x}-1)(x+\sqrt{x}+1))`
`=1/(\sqrt{x}-1)`
Xét `N=(1+\sqrt{x^3})/(1+\sqrt{x})-\sqrt{x}`
`=(1+\sqrt{x}^3)/(1+\sqrt{x})-\sqrt{x}`
`=((\sqrt{x}+1)(x-\sqrt{x}+1))/(\sqrt{x}+1)-\sqrt{x}`
`=x-\sqrt{x}+1-\sqrt{x}`
`=x-2\sqrt{x}+1`
`=(\sqrt{x}-1)^2`
Ta có: `B=M.N=1/(\sqrt{x}-1) . (\sqrt{x}-1)^2=\sqrt{x}-1`
b) `B=3`
`->\sqrt{x}-1=3`
`->\sqrt{x}=4`
`->x=16(TM)`
