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Cube root sum equality puzzle (Posted on 2015-06-09) Difficulty: 3 of 5
Find all pairs (a,b) of positive integers that satisfy this equation:

(∛A + ∛B -1)2 = 49 + 20*∛6

No Solution Yet Submitted by K Sengupta    
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Some Thoughts Thoughts Comment 2 of 2 |

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
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