2002 AMC 12P Problems/Problem 21
Problem
Let and be real numbers greater than for which there exists a positive real number different from , such that
Find the largest possible value of
Solution
We may rewrite the given equation as Since , we have , so we may divide by on both sides. After making the substitutions and , our equation becomes
Rewriting the left-hand side gives
Cross-multiplying gives or
Factoring gives or .
Recall that . Therefore, the maximum value of is .
See also
2002 AMC 12P (Problems • Answer Key • Resources) | |
Preceded by Problem 20 |
Followed by Problem 22 |
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All AMC 12 Problems and Solutions |
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