Question

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

Answer 1

I found `x=6`

Explanation:

We can try squaring both sides to get:
`(x-2)+2sqrt(x-2)sqrt(x+3)+(x+3)=25`
`x-2+2sqrt(x-2)sqrt(x+3)+x+3=25`
`2x+1+2sqrt(x-2)sqrt(x+3)=25`
rearranging:
`2sqrt(x-2)sqrt(x+3)=24-2x`
`sqrt(x-2)sqrt(x+3)=12-x`
square again:
`(x-2)(x+3)=144-24x+x^2`
`cancel(x^2)+3x-2x-6=144-24x+cancel(x^2)`
and:
`25x=150`
`x=6`