Question : If 'a' and 'b' are positive integers such that a2 – b2 = 19, then the value of 'a' is:
Option 1: 10
Option 2: 20
Option 3: 9
Option 4: 19
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Correct Answer: 10
Solution : a 2 – b 2 = 19 ⇒ (a + b)(a – b) = 19 × 1 Since 'a' and 'b' are positive integers, ⇒ a + b = 19 -------(i) and a – b = 1 ------(ii) Adding equations (i) and (ii), we get, 2a = 20 ⇒ a = 10 Hence, the correct answer is 10.
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