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Power Quady

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:
Full screen version

The idea came from a discussion between Toni Beardon and Bryan Dye (webmaster of MathsNet ) and the program has been written by Elizabeth Ayer.