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