`1)\sqrt{(5x+1)^2}=3`
`<=>(5x+1)^2=9`
`<=>25x^2+10x+1=9
`<=>25x^2+10x-8=0`
`<=>25x^2+20x-10x-8=0`
`<=>5x(5x+4)-2(5x+4)=0`
`<=>(5x+4)(5x-2)=0`
`<=>5x+4=0` hoặc `5x-2=0`
`<=>x=-4/5` hoặc `x=2/5`
Vậy `S={-4/5;2/5}`
`2)\sqrt{(x-1)^2}=\sqrt{(2x-3)^2}`
`<=>(x-1)^2=(2x-3)^2`
`<=>(x-1)^2-(2x-3)^1=0`
`<=>(x-1-2x+3)(x-1+2x-3)=0`
`<=>(2-x)(3x-4)=0`
`<=>x=2` hoặc `x=4/3`
Vậy `S={2;4/3}`
`3)\sqrt{2-5x}=4`
`<=>{(2-5x>=0),(2-5x=16):}`
`<=>{(x<=2/5),(5x=-1/8):}`
`<=>{(x<=2/5),(x=-1/8:5=-1/40(tm)):}`
Vậy `S={-1/40}`
`4)\sqrt{(3x-1)^2}=x+2`
`<=>{(x+2>=0),((3x-1)^2=(x+2)^2):}`
`<=>{(x>=-2),((3x-1)^2-(x+2)^2=0):}`
`<=>{(x>=-2),((3x-1-x-2)(3x-1+x+2)=0):}`
`<=>{(x>=-2),((2x-3)(4x+1)=0):}`
`<=>{(x>=-2),(x=3/2(tm) hoặc x=-1/4(tm)):}`
Vậy `S={3/2;-1/4}`
