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2006/07 AHSMC Part 1 Problem 9

Problem 9 of 16

If aa and bb are two real numbers which satisfy a+b−ab=1a + b - ab = 1 and aa is not an integer, then bb

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Solution

Solving for bb, we have b(1−a)=1−ab(1 - a) = 1 - a. Since aa is not an integer, 1−a≠01 - a \neq 0 and can be cancelled. Hence b=1b = 1, and is a positive integer. The answer is (b).

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