### System Speak

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

### Area L

By sketching a graph of a continuous increasing function, can you prove a useful result about integrals?

##### Stage: 5 Challenge Level:

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.