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
Answer (1)
23rd Jan, 2024
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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