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Find all real solutions of the equation (x^2-7x+11)^(x^2-11x+30) = 1.

### Golden Thoughts

Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.

### Two Cubes

Two cubes, each with integral side lengths, have a combined volume equal to the total of the lengths of their edges. How big are the cubes? [If you find a result by 'trial and error' you'll need to prove you have found all possible solutions.]

# Proof Sorter - Quadratic Equation

##### Age 14 to 18 Challenge Level:

Which statement follows on directly from $ax^2+bx+c=0$?

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