1987 AHSME Problems/Problem 10
Problem
How many ordered triples of non-zero real numbers have the property that each number is the product of the other two?
Solution
We have , , and , so multiplying these three equations together gives , and as , , and are all non-zero, we cannot have , so we must have . Now substituting gives . If , then the system becomes , so either or , giving solutions. If , the system becomes , so or , giving another solutions. Thus the total number of solutions is , which is answer .
See also
1987 AHSME (Problems • Answer Key • Resources) | ||
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Followed by Problem 11 | |
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