Find all pairs (a,b) of positive integers that satisfy this equation:

(∛A + ∛B -1)² = 49 + 20*∛6

If there are cube roots of 6 on RHS, then they must appear on LHS somewhere, say the natural substitution:

((a)^(1/3)+ (6a)^(1/3)-1)^2 =49+20*6^(1/3)

WolframAlpha gives a=48, from which Charlie's solutions can be derived.

Incidentally, the cube root of 48 is 2*6^(1/3) and of 288 is 2*6^(2/3)

Posted by broll on 2015-06-10 07:22:32