`1. sqrt((x-3)^2)=3-x`
`<=>|x-3|=3-x`
`text(TH1):x>=3`
`x-3=3-x`
`<=>x-3-3+x=0`
`<=>2x-6=0`
`<=>2x=6`
`<=>x=3(loại)`
`text(TH2):x<3`
`x-3=-(3-x)`
`<=>x-3=-3+x`
`<=>x-3+3-x=0`
`<=>0x=0(loại)`
Vậy phương trình vô nghiệm.
`2.sqrt(1-12x+36x^2)=5`
`<=>sqrt((1-6x))^2=5`
`text(TH1):x>=1/6`
`1-6x=5`
`<=>-6x=4`
`<=>x=-2/3(TM)`
`text(TH2):x<1/6`
`1-6x=-5`
`<=>-6x=-6`
`<=>x=1(TM)`
Vậy `x=1`
`3.sqrt(x−2sqrtx+1)=2`
`<=>sqrt((sqrtsx−1)^2)=2`
`<=>|sqrtx−1|=2`
`text(TH1):x>=1`
`<=>sqrtx−1=2`
`<=>sqrtx=3`
`<=>x=9(TM)`
`text(TH2): 0<x<1`
`<=>1−sqrtx=2`
`<=>sqrtx=-1(loại)`
Vậy `x=9`
`4.sqrt(4x^2-20x+25+2x)=5`
`<=>sqrt(4x^2-18x+25)=5`
`<=>4x^2-18x+25=25`
`<=>4x^2-18x=0`
`<=>2x(2x-9)=0`
`<=>`\(\left[ \begin{array}{l}2x=0\\2x-9=0\end{array} \right.⇔\left[ \begin{array}{l}x=0\\x=\dfrac92\end{array} \right.\)
Vậy `x=9/2`
