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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.

Submit your solution

Please do send in your solution to this problem to  You can scan or photograph your written work, or type your solutions. If this is your first weekly maths challenge solution, please include your year group and the name of the school you attend. We'll be happy to provide feedback on your solution, assuming that you are in year 11 or below. If you are older than this, we hope you enjoy trying the problems and reviewing your solutions against those we publish on the website.