Common pitfall in A-level math #1

In 2013 A-level Paper 2 , many students made an unfortunate mistake. The following is an snapshot of questions 2 of the paper.

Credits: 2013 A-level

Credits: 2013 A-level

Many students faced the dilemma of what to prove, and some resorted to asking the invigilators who were non-math trained. They were uncertain about how to treat the squareroot, like is it \sqrt{3}(a-2x\sqrt{3})^2 or \sqrt{3(a-2x\sqrt{3})^2} So students need to learn to rationalise what the question is asking, on the spot. Alert students will notice is the latter will be definitely wrong, since the squareroot will have simplified the square in the expression.

Recall from primary school, we learnt the BODMAS rule which will come in handy in analysing this question.

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