De, Prithwijit
(2017)
On problem posing.
At Right Angles, 6 (2).
pp. 82-85.
ISSN 2582-1873
Abstract
Problem-posing and problem-solving are central
to mathematics. As a student one solves a plethora
of problems of varying levels of difficulty to learn the
applications of theories taught in the mathematics
curriculum. But rarely is one shown how problems are made.
The importance of problem-posing is not emphasized as a
part of learning mathematics. In this article, we show how
new problems may be created from simple mathematical
statements at the secondary school level.
We begin with a simple problem.
Problem. Let a, b, c be three positive real numbers. Prove that
a
b
c
3
+
+
≥ .
(1)
b + c c + a a + b
2
This is known as Nesbit’s inequality.
Proof. There are several proofs of this statement. One of
them uses the arithmetic mean-harmonic mean (AM-HM)
inequality (see Box 1). If we call the algebraic expression on
the left hand side P, then by adding 1 to each term we get:
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