SOLUTION: barney chose two numbers a and b with 0 < a < b < 1. He decided to combine the numbers and wrote down a+b, b-a, a-b, a/b, b/a and ab. He saw that he had written the same n

Question 446590: barney chose two numbers a and b with 0 < a < b < 1.
He decided to combine the numbers and wrote down a+b, b-a, a-b, a/b, b/a and ab.
He saw that he had written the same number down twice and, even more surprisingly, that he had also written a second number down twice.
What were his possible starting numbers
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Best way would be to identify the range of each number (e.g. 0 < a+b < 2, etc.) by using extreme cases. The problem will become fairly tedious though. You could also try graphing various equations or trying substitutions (e.g. letting a = sin x, b = cos y) that make the problem no less different.
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