A blog about Mathematics and Mathematics Education in Singapore, as well as Mathematics Education in general. Written for students, parents, educators and other stakeholders in Singapore, and around the world.
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Friday, April 10, 2015
[AM_20150409ASD] Absurd Surds!
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
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.