Community Mathematics Centre, CoMaC
(2020)
An ‘extreme algebra’ question.
At Right Angles.
pp. 99101.
ISSN 25821873
Abstract
We came across this problem in a Facebook post which in turn pointed to a YouTube video. Given that a, b, c are numbers such that a + b + c = 1, a2 + b2 + c2 = 2 and a3 + b3 + c3 = 3, find the value of a5 + b5 + c5. The author describes this as an ‘extreme algebra’ problem, as the solution involves an ‘extreme amount’ of algebra. He solves the problem in a direct, straightforward manner, by multiplying the corresponding sides of the second and third equalities (thereby getting the expression a5 + b5 + c5) and then somehow getting rid of the unwanted terms.
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