1988 AHSME Problems/Problem 26
Contents
Problem
Suppose that and are positive numbers for which What is the value of ?
Solution 1
We can rewrite the equation as . Then, the system can be split into 3 pairs: , , and . Cross-multiplying in the first two, we obtain: and Adding these equations results in: which simplifies to Dividing by on both sides gives: . We set the desired value, to and substitute it into our equation: which is solved to get our answer: . -lucasxia01
Solution 2
For some number t:
Next we can divide by to obtain
Furthermore, we know that
and
Substituting into the previous equation, we get
Let and we can observe that , then similarly to solution 1: , in which we get: - ehmmaq
See also
1988 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 25 |
Followed by Problem 27 | |
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