AoPS Wiki talk:Problem of the Day/July 21, 2011
Problem
AoPSWiki:Problem of the Day/July 21, 2011
Solution
Note: someone check the arithmetic please
For purposes of generalization, let the equations be and
. Notice that
. Swap this out for a new variable
.
This gives
.
Multiply the left equation by two and substitute it into the other equation.
, which implies that
. Substituting the actual numbers back in gives:
Simplifying:
Which further simplifies to:
Then we just plug this back into the original parameter, where .
And we find that the only solution is