## Challenge 330: Root out the Problem

√(3x – 2) - √(2x – 3) = 1

A misguided student submitted the following solution to the equation above

They wrote

“Squaring both sides gives 3x – 2 – 2x – 3 = 1

Therefore x – 5 = 1

So **x = 6** "

(i) Is their answer correct? What is wrong with their solution?

(ii) Find an equation in the same format which gives an **incorrect** answer using this method.

(iii) Find another equation in the same format which gives the **correct** answer using this method.