Question

What is the sum of two consecutive odd numbers the difference of whose square is 64?

Answer 1

• Let one odd consecutive number be M and other be M + 2.

» The difference of square of these two consecutive odd numbers (i.e. M and M + 2) is 64.

=> M² - (M - 2)² = 64

(a - b)² = a² + b² - 2ab

=> M² -(M² + 4 - 4M) = 64

=> M² - M² + 4 + 4M = 64

=> 4M = 60

=> M = 15

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• The one consecutive odd number is (M)

=> 15

• And other is (M + 2)

=> 17 (15 + 2).

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» We have to find the sum of odd consecutive Numbers.

From above calculations the two odd consecutive numbers that we get are 15 and 17.

Now we have to add both the numbers.

=> 15 + 17 = 32.

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The sum of two consecutive odd numbers is 32.

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