median
don steward
mathematics teaching 10 ~ 16

Sunday, 19 December 2010

d(23)

two numbers are d(23) if

a x b - (a + b) = 23

the task is to find two numbers so that the difference between the product and the sum of these is 23

can students find the four pairs of integers ('a' and 'b') that fit this rule?

can they find some rational solutions?


 the intention of this task is that students substitute numbers by trial and improvement
and hopefully appreciate the symmetry of results

however, if they were to add 1 to both sides
the problem is solved quite simply algebraically
by factorising

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