Question

How do you solve `sqrt(2x-1) - sqrt(x+7) = 0`?

Answer 1

`x=8`

Explanation:

`sqrt(2x-1) - sqrt(x+7) = 0`

`=>sqrt(2x-1) = sqrt(x+7)`

`=> 2x-1 = x+7`

`=> 2x-x = 7+1`

`=> x = 8`

Answer 2

`x=8`

Explanation:

`color(blue)(sqrt(2x-1)-sqrt(x+7)=0`

Add `sqrt(x+7)` both sides

`rarrsqrt(2x-1)=sqrt(x+7)`

Square both sides to get rid of the radical sign

`rarr(sqrt(2x-1))^2=(sqrt(x+7))^2`

`rarr2x-1=x+7`

Subtract `x` both sides

`rarrx-1=7`

`color(green)(rArrx=7+1=8`

Check

`color(brown)(sqrt(2(8)-1)-sqrt(8+7)=0`

`color(brown)(sqrt(16-1)-sqrt(8+7)=0`

`color(brown)(sqrt15-sqrt15=0`

So,It is true