`a) \sqrt{4x^2 - 12x +9} =7`
`=> \sqrt{(2x)^2 - 2.3.2x +3^2} = 7`
`=>\sqrt{ (2x -3)^2} = 7`
`=> |2x -3| = 7`
`=>`\(\left[ \begin{array}{l}2x -3 =7\\2x -3 =-7\end{array} \right.\)
`=>`\(\left[ \begin{array}{l}2x = 10\\2x = -4\end{array} \right.\)
`=>`\(\left[ \begin{array}{l}x=5\\x=-2\end{array} \right.\)
Vậy phương trình có nghiệm `S = {5;-2}`
`b) \sqrt{x -10\sqrt{x} +25} = 3`
`=> \sqrt{\sqrt{x}^2 - 2.5.\sqrt{x} +5^2} = 3`
`=> \sqrt{ (\sqrt{x} - 5}^2} =3`
`=> |\sqrt{x} -5| =3`
`=>`\(\left[ \begin{array}{l}\sqrt{x} -5 =3\\\sqrt{x} -5 =-3\end{array} \right.\)
`=>` \(\left[ \begin{array}{l}\sqrt{x} =8\\\sqrt{x} =2\end{array} \right.\)
`=>`\(\left[ \begin{array}{l}x=64\\x=4\end{array} \right.\)
Vậy phương trình có nghiệm `S={64;4}`
Câu trên đề :
`\sqrt{4x^2 -4x +1} = \sqrt{ x^2 -2x +1}`
`=> \sqrt{(2x)^2 - 2.2x +1}=\sqrt{(x-1)^2}`
`=> \sqrt{(2x -1)^2} = \sqrt{(x-1)^2}`
`=> |2x -1| = |x -1|`
`=> `\(\left[ \begin{array}{l}2x -1=x-1\\2x -1 =-(x-1)\end{array} \right.\)
`=>` \(\left[ \begin{array}{l}x =2x\\2x -1 =-x+1\end{array} \right.\)
`=>`\(\left[ \begin{array}{l}x=0\\3x=2\end{array} \right.\)
`=>`\(\left[ \begin{array}{l}x=0\\x=3/2\end{array} \right.\)
Vậy phương trình có nghiệm `S={0;3/2}`
