Stage: 4 Challenge Level: 
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.]
Surds. Polynomials. Factorisation (algebraic). Long problems. Inequality/inequalities. Mathematical reasoning & proof. Quadratic equations. Stage 5 - Reviewed 2012. Golden ratio. epsilons.
Published September 1999.
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