`\sqrt{x^2-2x+1}=x^2-1` (1)
ĐKXĐ: `x>=1` hoặc `x<=-1`
`(1)<=> \sqrt{(x-1)^2}=x^2-1`
`<=> |x-1|=x^2-1`
Với `x>=1` thì
`x-1=x^2-1`
`<=> x^2-x=0`
`<=> x(x-1)=0`
`<=>`\(\left[ \begin{array}{l}x=0(l)\\x=1(TM)\end{array} \right.\)
Với `x<=-1` thì
`1-x=x^2-1`
`<=> x^2+x-2=0`
`<=> x^2-x+2x-2=0`
`<=> (x-1)(x+2)=0`
`<=>`\(\left[ \begin{array}{l}x=1(l)\\x=-2(TM)\end{array} \right.\)
Vậy `S={1;-2}`
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`\sqrt{4x^2-4x+1}=x+1` (2)
ĐKXĐ: `x>=-1`
`(2)<=> 4x^2-4x+1=(x+1)^2`
`<=> 4x^2-4x+1=x^2+2x+1`
`<=> 3x^2-6x=0`
`<=> 3x(x-2)=0`
`<=>`\(\left[ \begin{array}{l}x=0(TM)\\x=2(TM)\end{array} \right.\)
Vậy `S={0;2}`
