Question

Giải pt:

\(\sqrt{x^2-3x+2}+\sqrt{x+3}=\sqrt{x-2}+\sqrt{x^2+2x-3}\)

Answer 1

`ĐK:x>=2`

`pt<=>sqrt{(x-1)(x-2)}+sqrt{x+3}=sqrt{x-2}+sqrt{(x-1)(x+3)}`

`<=>sqrt{x-1}(sqrt{x-2}-sqrt{x+3})-(sqrt{x-2}-sqrt{x+3})=0`

`<=>(sqrt{x-2}-sqrt{x+3})(sqrt{x-1}-1)=0`

`+)sqrt{x-2}=sqrt{x+3}`

`<=>x-2=x+3`

`<=>0=5` vô lý

`+)sqrt{x-1}-1=0`

`<=>x-1=1`

`<=>x=2(tm)`.

Vậy `x=2`.