Solve the system

5^(y-x)*(y+x) = 1
and
(x+y)^(x-y) = 5

If (x-y)=a and (x+y)=b, the problem is

b/5^a = 1
b^a = 5

From the first, b=5^a, so in the second (5^a)^a=5, so a^2=1, and b=5^a.

If a=1, b=5; solving backwards, x=3 and y=2.
If a=-1, b=1/5; solving backwards, x=-2/5 and y=3/5.

Posted by e.g. on 2005-05-16 14:34:29