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There are two whole numbers, difference of their squares is a cube and difference of their cube is a square...

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There are two whole numbers, difference of their squares is a cube and difference of their cube is a square. These are the smallest possible numbers. can you find the numbers?

posted Mar 28, 2016 by Vinni Fernandis

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2 Answers

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The numbers are 6 & 10.

6*6 - 10*10 = 64, which is cube of 4
6*6*6 - 10*10*10 = 784, which is square of 28.

answer Mar 28, 2016 by Kunal Shah
0 votes

The numbers are 10 and 6.
10 squared (100) - 6 squared (36) = 64, which is 4-cubed
10 cubed (1000) - 6 cubed (216) = 784, which is 28-squared.

answer Mar 31, 2016 by Sundararajan Srinivasa Gopalan
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