Question

The difference is the square of two consecutive natural numbers is 65.what is the number?

Answer 1

Answer :

• The numbers are 32 and 33

Given :

• The difference is the square of two consecutive natural numbers is 65

To find :

• The numbers

Solution :

• Let the number be x
• Other number be x + 1

Given, the difference is the square of two consecutive natural numbers is 65 so,

➠ (x + 1)² - x² = 65

➠ x² + 2x + 1 - x² = 65

➠ 2x = 65 - 1

➠ 2x = 64

➠ x = 64/2

➠ x = 32

Hence , The numbers are 32 and 33

Verification :

➠ (x + 1)² - x² = 65

➠ (32 + 1)² - (32)² = 65

➠ (33)² - 1024 = 65

➠ 1089- 1024 = 65

➠ 65 = 65

Hence verified