Question:
How many different pairs (a, b) of positive integers are there such that a ≤ b and 1/a+1/b=1/9=?
How many different pairs (a, b) of positive integers are there such that a ≤ b and 1/a+1/b=1/9=?
Updated On: Sep 26, 2024
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The Correct Option is B
Solution and Explanation
1/a+1/b = 1/9
⇒ 9(a + b) = ab
⇒ ab – 9a – 9b + 81 = 81
⇒ (a – 9) (b – 9) = 81 = 34
As a, b > 0 and a ≤ b, there are only 3 ordered pairs, given by a – 9 = 1, 3 or 9 and correspondingly b – 9 = 81, 27, 9.
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