**Question**

**Introduction**

This looks
like a dastardly absurd problem on surds.
If you tried to do this question by direct calculation, you might get
the correct answer after a long series of working, provided you do not make
careless mistakes.

Is there a
better way to do it? You bet! First we simplify

*x*as much as possible. [H10] Secondly, look for relationships or patterns. [H04] Note that*y*is the “inverted” version of*x*, so*y*is the**of***reciprocal**x*. Thirdly, use more algebra [H13] instead of just calculating like a donkey. Some useful algebraic identities are*x*^{3}+*y*^{3}= (*x*+*y*)(*x*^{2}–*xy*+*y*^{2}), and*x*^{2}+*y*^{2}= (*x*+*y*)^{2}– 2*xy*.**Solution**

H04. Look for pattern(s)

H09. Restate the problem in
another way

H10. Simplify the problem

H11. Solve part of the problem

H13* Use Equation / write a
Mathematical Sentence

**Suitable Levels**

*****GCE ‘O’ Level Additional Mathematics

* anyone who is interested in surds, even if it seems absurd.

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