Question

The sum of the square of the 2 consecutive natural numbers is 481. Find the numbers.

Answer 1

Let these numbers be A and A+ 1.

Then as per the question, A² + (A+1)² = 481 

⇒ A² + A² + 2A + 1 = 481

⇒ 2 A² + 2A - 480 = 0

⇒ A² + A - 240 = 0

⇒ A² + 16 A - 15 A - 240 = 0

⇒ A (A + 16) - 15 (A + 16) = 0

⇒ (A - 15) (A + 16) = 0

⇒ A = 15 , -16 (-16 is not a natural number)

⇒ A=15 

⇒ Hence the numbers are 15 and 16.