Question

How do you solve `\sqrt { 5x + 3} = \sqrt { 9x - 3}`?

Answer 1

`x=3/2`

Explanation:

Given:

`sqrt(5x+3)=sqrt(9x-3)`

Note that both sides of the equation are non-negative for non-negative radicands. So without introducing extraneous solutions, we can square both sides to get:

`5x+3=9x-3`

Add `3-5x` to both sides to get:

`6 = 4x`

Divide both sides by `4` and transpose to get:

`x = 6/4 = 3/2`