1990 AIME Problems/Problem 4
From AoPSWiki
Problem
Find the positive solution to
Solution
We could clear out the denominators by multiplying, though that would be unnecessarily tedious.
To simplify the equation, substitute 
(the denominator of the first fraction). We can rewrite the equation as 
. Multiplying out the denominators now, we get:
Simplifying, 
, so 
. Re-substituting, 
. The positive root is 
.
See also
| 1990 AIME (Problems • Resources) | ||
| Preceded by Problem 3 | Followed by Problem 5 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
