√(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.