How many pairs of natural numbers are there such that the difference of whose squares is 63 ........

Math and Mental Ability Number System

How many pairs of natural numbers are there such that the difference of whose squares is 63?

This questions was previously asked in

Complete-Test, Previous year (2020)

Sol. Ans.(a).

Natural numbers are integers starting with 1.

Let the two numbers be a and b then

a² – b² = 63 =>(a + b) (a – b) = 63. Now 63 = 9 × 7 = 21 × 3 = 63 × 1 So,

Case I: a + b = 9; a – b = 7. Here we will get a = 8 and b = 1

Case II: a + b = 21; a – b = 3. Here we will get a = 12 and b = 9.

Case III: a + b = 63; a – b = 1. Here we will get a = 32 and b = 31

Since 63 has only these 3 pairs of factors, so the correct option is (a).

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