Q22 of 47 Page 1

Find two consecutive odd natural numbers, the sum of whose squares is 394.

Let the odd natural numbers be 2x – 1 and 2x + 1

Now according to the question,


(2x – 1)2 + (2x + 1)2 = 394


⇒ 4x2 – 4x + 1 + 4x2 + 4x + 1 = 394


⇒ 8x2 + 2 = 394


⇒ 8x2 = 394 – 2


⇒ 8x2 = 392



⇒ x2 = 49


⇒ x= √49


⇒ x= 7


∴


2x – 1 = 2 × 7 – 1 = 14 – 1 = 13


2x + 1 = 2 × 7 + 1 = 14 + 1 = 15


Hence, the consecutive odd natural numbers are 13 and 15.


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