SOLUTION: If a^3+12ab^2=679 and 9a^2b+12b^3=978, find (a-2b)^2.

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Question 1120936: If a^3+12ab^2=679 and 9a^2b+12b^3=978, find (a-2b)^2.
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


I looked at this problem several times before I realized how easy it was, with the help of a graphing calculator....

The given equations suggest that a and b are both integers, probably positive.

So solve the first equation for b in terms of a; then use a graphing calculator table to find an integer value of a that gives a perfect square integer value for b^2.

b%5E2+=+%28679-a%5E3%29%2F%2812a%29

My TI-83 calculator shows b^2=4 when a = 7; the apparent solution is a=7 and b=2.

Plugging those values in the two given equations confirms the answer.

So the answer to the problem is:
(a-2b)^2 = (7-4)^2 = 9