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My question is:

Solve for $a$, $b$, and $c$ if: $$a^2 - b^2=36,$$ $$b^2 - c^2=\frac{116}{3},$$ $$a^2 - c^2=\frac{224}{3}.$$

Any solution for this question would be greatly appreciated.

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    Consider any two of the three equations. The third equation can be derived from the other two, and so gives you no more information about the unknowns. So you have two equations with 3 unknowns and so the best you can do is write a in terms of b and c (for example)2012-07-09
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    If this is truly a Diophantine equation, your solution set is empty.2012-07-09
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    To see this more directly, let's just look at equations 1 and 2 and ignore the 3rd for a moment. Consider a = 10, Then b and c can both take two values (b can take +-8 and c can take +-(sqrt(73/3)). These values of c will satisfy the 3rd equation (check). Moreover, for ANY value of a >= 6, b and c will be uniquely determined (up to +-)2012-07-09
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    Surely if this is a diophantine equation then the question is silly2012-07-09
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    hey all sorry yes this is not a diophantine equation...i tagged it wrong2012-07-09

3 Answers 3