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Mega Quadratic Equations

Stage: 5 Challenge Level: Challenge Level:1

There are six possible solutions to each of the following equations. Can you find them all?

1. $(n^2 - 5n + 5)^{(n^2 - 11n + 30)} = 1$

2. $(n^2 - 7n + 11)^{(n^2 - 13n + 42)} = 1$

Can you find some more Mega Quadratic Equations like these?



With thanks to Don Steward, whose ideas formed the basis of this problem.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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