SOLUTION: Let and be relatively prime integers with a > b > 0 and (a^3 - b^3)/(a-b)^3= 73/3. What is a-b?

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Question 1160416: Let and be relatively prime integers with a > b > 0 and (a^3 - b^3)/(a-b)^3= 73/3. What is a-b?
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


%28a%5E3+-+b%5E3%29%2F%28a-b%29%5E3=+73%2F3

%28%28a-b%29%28a%5E2%2Bab%2Bb%5E2%29%29%2F%28a-b%29%5E3+=+73%2F3

%28a%5E2%2Bab%2Bb%5E2%29%2F%28a%5E2-2ab%2Bb%5E2%29+=+73%2F3

73a%5E2-146ab%2B73b%5E2+=+3a%5E2%2B3ab%2B3b%5E2

70a%5E2-149ab%2B70b%5E2+=+0

%287a-10b%29%2810a-7b%29+=+0

7a+=+10b or 10a+=+7b

Then, since a and b are relatively prime integers with a > b > 0, a = 10 and b = 7.

And so a-b = 3.

ANSWER: a-b = 3