SOLUTION: a�+b�=25 a�+b�=91

Question 691044: a�+b�=25
a�+b�=91
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
I am not sure if the problem is meant as a system of non-linear equations, or a simpler problem, looking for integers that satisfy each (or both) equations.

The most popular of Pythagorean triples (and the only one I remember) is
(3,4,5) with or .
So the only answer to with whole numbers is . If we allow negative numbers, there are other integer solutions to just that equation (we just cahnge the signs for a and/or b).

Curiously, the same numbers 3 and 4 are a solution to ,
.
So you could say that the pair (3,4) is the only integer solution to the system

If we wanted all real numbers that are solutions to the system, we would have to look for two more points where the graphs intersect for
(circle with radius 5) and
<--> (a snakey downwards line).
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