`1)\sqrt{9x^2-12x+4}=\sqrt{x^2}`
`<=>\sqrt{(3x-2)^2}=\sqrt{x^2}`
`<=>|3x-2|=|x|`
`<=>[(3x-2=x),(3x-2=-x):}`
`<=>[(x=1),(x=1/2):}`
Vậy `S={1;1/2}`
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`2)\sqrt{x^2-4x+4}=\sqrt{4x^2-12x+9}`
`<=>\sqrt{(x-2)^2}=\sqrt{(2x-3)^2}`
`<=>|x-2|=|2x-3|`
`<=>[(x-2=2x-3),(x-2=3-2x):}`
`<=>[(x=1),(x=5/3):}`
Vậy `S={1;5/3}`
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`3)\sqrt{x+2\sqrt{x-1}}=2` `ĐK: x >= 1`
`<=>\sqrt{(\sqrt{x-1}+1)^2}=2`
`<=>|\sqrt{x-1}+1|=2`
`<=>[(\sqrt{x-1}+1=2),(\sqrt{x-1}+1=-2):}`
`<=>[(\sqrt{x-1}=1),(\sqrt{x-1}=-3(VN)):}`
`<=>\sqrt{x-1}=1`
`<=>x-1=1<=>x=2` (t/m)
Vậy `S={2}`
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`4)\sqrt{x+2\sqrt{x-1}}-\sqrt{x-2\sqrt{x-1}}=2` `ĐK: x >= 1`
`<=>\sqrt{(\sqrt{x-1}+1)^2}-\sqrt{(\sqrt{x-1}-1)^2}=2`
`<=>|\sqrt{x-1}+1|-|\sqrt{x-1}-1|=2`
`<=>\sqrt{x-1}+1-|\sqrt{x-1}-1|=2`
`@TH1:\sqrt{x-1}-1 >= 0<=>\sqrt{x-1} >= 1<=>x-1 >= 1<=>x >= 2`
`=>\sqrt{x-1}+1-\sqrt{x-1}+1=2`
`<=>0x=0` (LĐ)
Kết hợp `x >= 2`
`=>x >= 2`
`@TH2:\sqrt{x-1}-1 < 0<=>\sqrt{x-1} < 1<=>x-1 < 1<=>x < 2` Kết hợp đk
`=>1 <= x < 2`
`=>\sqrt{x-1}+1-1+\sqrt{x-1}=2`
`<=>2\sqrt{x-1}=2`
`<=>\sqrt{x-1}=1`
`<=>x-1=1`
`<=>x=2` (ko t/m)
Vậy `S={x >= 2}`
