Friday, April 10, 2015

[AM_20150409ASD] Absurd Surds!

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)(x2xy + 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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