Question 1120936
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I looked at this problem several times before I realized how easy it was, with the help of a graphing calculator....<br>
The given equations suggest that a and b are both integers, probably positive.<br>
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.<br>
{{{b^2 = (679-a^3)/(12a)}}}<br>
My TI-83 calculator shows b^2=4 when a = 7; the apparent solution is a=7 and b=2.<br>
Plugging those values in the two given equations confirms the answer.<br>
So the answer to the problem is:
(a-2b)^2 = (7-4)^2 = 9