`a)` `\sqrt{x-2011}=3` ĐKXĐ: `x\geq2011`
`<=>(\sqrt{x-2011})^2=3^2`
`<=>x-2011=9`
`<=>x=9+2011`
`<=>x=2020` (TM)
Vậy `x=2020`
`b)` `3\sqrt{4x+12}-\sqrt{9x+27}+\sqrt{x+3}=8` ĐKXĐ: `x\geq-3`
`<=>3\sqrt{4(x+3)}-\sqrt{9(x+3)}+\sqrt{x+3}=8`
`<=>3.\sqrt{4}.\sqrt{x+3}-\sqrt{9}.\sqrt{x+3}+\sqrt{x+3}=8`
`<=>6\sqrt{x+3}-3\sqrt{x+3}+\sqrt{x+3}=8`
`<=>4\sqrt{x+3}=8`
`<=>\sqrt{x+3}=2`
`<=>(\sqrt{x+3})^2=2^2`
`<=>x+3=4`
`<=>x=4-3`
`<=>x=1` (TM)
Vậy `x=1`
`d)` `\sqrt{4x^2-12x+9}=5`
`<=>\sqrt{(2x-3)^2}=5`
`<=>|2x-3|=5`
`<=>` \(\left[ \begin{array}{l}2x-3=5\\2x-3=-5\end{array} \right.\)`<=>` \(\left[ \begin{array}{l}2x=8\\2x=-2\end{array} \right.\)`<=>` \(\left[ \begin{array}{l}x=4\\x=-1\end{array} \right.\)
Vậy `x=4;x=-1`
