Question

Giải phương trình:

`x+1=2.sqrt(x) + sqrt(x-3)`

Answer 1

Đk: `x>=3`.

`@ x+1=2 sqrt x + sqrt(x-3)`

`<=> x+1= (4x-x+3)/(2sqrtx-sqrt(x-3))`

`<=> x+1=(3x+3)/(2sqrtx-sqrt(x-3))`

`<=> (x+1).(1-3/(2sqrtx-sqrt(x-3)))=0`

`<=> x=-1 (ktm)` hoặc `2sqrtx-sqrt(x-3)=3 (1)`

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

`<=> 4x=9+6sqrt(x-3)+x-3`

`<=> x-2=2sqrt(x-3)`

`<=> x-2sqrt(x-3)-2=0`

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

`<=> (sqrt(x-3)-1)^2=0`

`<=> sqrt(x-3)=1`

`<=> x=4`

Vậy `x=4`.