a,b,c are positive integers forming an increasing G.P and b-a is a perfect cube and + + =6 then a+b+c=?

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- August 8th 2010, 05:18 PMgrgrsanjaylogarithms question ♥
a,b,c are positive integers forming an increasing G.P and b-a is a perfect cube and + + =6 then a+b+c=?

- August 8th 2010, 05:28 PMeumyang

If a, b, and c form a geometric progression then b = ar and c = ar^2 (for some ratio r):

has to be a perfect cube, or has to be a perfect cube. There are a few possibilities for a (35, 28, 9), but the only one that will work in our case is if a = 9.

If a = 9 and b = 36, then r = 4, which makes c = 144. So a + b + c = 189.