Câu `3:`

`a) sqrt((x+2)/(x-1))=3 \ ((x+2)/(x-1)ge0,xne1)`

`(x+2)/(x-1)=9`

`x+2=9(x-1)`

`x+2=9x-9`

`8x=11`

`x=11/8` (thỏa mãn)

Vậy `x=11/8`

`b) sqrt((2x-3)/(x+1))=2 \ ((2x-3)/(x+1)ge0,xne-1)`

`(2x-3)/(x+1)=4`

`2x-3=4(x+1)`

`2x-3=4x+4`

`-2x=7`

`x=-7/2` (thỏa mãn)

Vậy `x=-7/2`

`c) sqrt(1-x/(x+5))=4 \ (1-x/(x+5)ge0,xne-5)`

`1-x/(x+5)=16`

`(x+5-x)/(x+5)=16`

`5/(x+5)=16`

`16(x+5)=5`

`16x+80=5`

`16x=-75`

`x=-75/16` (thỏa mãn)

Vậy `x=-75/16`

`d) sqrt(5+(x-3)/x)=1/2 \ (5+(x-3)/xge0,xne0)`

`5+(x-3)/x=1/4`

`(x-3)/x=1/4-5=-19/4`

`4(x-3)=-19x`

`4x-12=-19x`

`23x=12`

`x=12/23` (thỏa mãn)

Vậy `x=12/23`

`e) 3sqrt((2x)/(x+1))-1=5 \ ((2x)/(x+1)ge0,xne-1)`

`3sqrt((2x)/(x+1))=6`

`sqrt((2x)/(x+1))=2`

`(2x)/(x+1)=4`

`2x=4(x+1)`

`2x=4x+4`

`-2x=4`

`x=-2` (thỏa mãn)

Vậy `x=-2`

`f) sqrt(x^2/(x-2)-x)=3 \ (x^2/(x-2)-xge0,xne2)`

`x^2/(x-2)-x=9`

`(x^2-x(x-2))/(x-2)=9`

`(x^2-x^2+2x)/(x-2)=9`

`(2x)/(x-2)=9`

`2x=9(x-2)`

`2x=9x-18`

`-7x=-18`

`x=18/7` (thỏa mãn)

Vậy `x=18/7`

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