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System Speak

Five equations... five unknowns... can you solve the system?

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.