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 reciprocal of x. Thirdly, use more algebra [H13] instead of just calculating like a donkey. Some useful algebraic identities are x3 + y3 = (x + y)(x2
– xy + y2), and x2 + y2 = (x + y)2 – 2xy.
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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