Đáp án + Giải thích các bước giải:
a)
`\sqrt{x-1}=2`
`=>x-1=4`
`=>x=5`
b)
`\sqrt{3(2x+1)}=3`
`=>3(2x+1)=9`
`=>2x+1=3`
`=>2x=2`
`=>x=1`
c)
`\sqrt{1-x}=-1`
`\sqrt{1-x}\ge0` mà `-1<0`
`=>x∈∅`
d)
`x-2\sqrtx=0`
`=>\sqrtx(\sqrtx-2)=0`
`=>` \(\left[ \begin{array}{l}\sqrt{x}=0\\\sqrt{x}-2=0\end{array} \right.\)
`=>` \(\left[ \begin{array}{l}x=0\\\sqrt{x}=2\end{array} \right.\)
`=>` \(\left[ \begin{array}{l}x=0\\x=4\end{array} \right.\)
Vậy `x∈{0;4}`
e)
`x=-2\sqrt{x}`
`=>x+2\sqrt{x}=0`
`=>\sqrt{x}(\sqrt{x}+2)=0`
`=>` \(\left[ \begin{array}{l}\sqrt{x}=0\\\sqrt{x}+2=0\end{array} \right.\)
`=>` \(\left[ \begin{array}{l}x=0\\\sqrt{x}=-2\end{array} \right.\)
`\sqrt{x}\ge0` mà `-2<0`
`=>x=0`
f)
`x=\sqrtx`
`=>x-\sqrtx=0`
`=>\sqrt{x}(\sqrtx-1)=0`
`=>` \(\left[ \begin{array}{l}\sqrt{x}=0\\\sqrt{x}-1=0\end{array} \right.\)
`=>` \(\left[ \begin{array}{l}x=0\\\sqrt{x}=1\end{array} \right.\)
`=>` \(\left[ \begin{array}{l}x=0\\x=1\end{array} \right.\)
Vậy `x∈{0;1}`
