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

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

  1. 3
  2. 4
  3. 5
  4. 2
  • Answer: The correct option is A
  • Explanation:

    Let the required pair of natural number is x and y.

    As per the question,

    x2 - y 2 = 63

    (x + y)(x - y) = 63

    There are three possible cases in which product of two numbers is 63.

    Case 1:

    (x + y) = 9 and (x - y) = 7

    Then x = 8 and y = 1

    Case 2:

    (x + y) = 21 and (x - y) = 3

    Then x = 12 and y = 9

    Case 3:

    (x + y) = 63 and (x - y) = 1

    Then x = 32 and y = 31
  • Exam Year: 2020