Question

How do you solve: `sqrt(2x+5) - sqrt(x-2) = 3`?

Answer 1

`sqrt(2x+5) - sqrt(x-2)=3`

1. First isolate one of the square roots:
   `sqrt(2x+5)=3+sqrt(x-2)`

2. Then square each side:
   `(sqrt(2x+5))^2=(3+sqrt(x-2))(3+sqrt(x-2))`
   `2x+5=9+6sqrt(x-2)+(x-2)`

3. Simplify the equations leaving the square root on one sided:
   `x-2=6sqrt(x-2)`

4. Square each side:
   `(x-2)(x-2)=36(x-2)`

5. Divide each side by (x-2):
   `x-2=36`
   so `x=38`

All ways check you answer in the original problem:
`sqrt(2x+5) - sqrt(x-2)=3`
`sqrt(2(38)+5) - sqrt(38-2)=3`
`sqrt(81) - sqrt(36)=3`
`9-6=3`
`3=3`