1.

a and b are two natural numbers such that a2 - b2 is a prime number. Then the value of a2 - b2 is1. a - b2. a + b3. ab4. None of the above

Answer» Correct Answer - Option 2 : a + b

Concept

A Prime number is a number divisible by 1 and itself only. 

a2 - b2 = (a - b)(a + b)

Calculation

a2 - b2 = (a - b)(a + b) is a prime

So, it is divisible by 1 and itself 

So, either (a - b) = 1 or (a + b) = 1

But (a + b) ≠ 1 {a and b are natural numbers}

∴ (a - b) = 1

⇒ a2 - b2 = (1)(a + b) = a + b


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