Find two consecutive odd positive integers, sum of whose squares is 970.

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41,43

21,23

10,20

20,11

answer is B.

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Detailed Solution

Given: Sum of two odd positive consecutive integers is 970.
Assume that the two consecutive positive integers be x and x+2.
According to the question,

⇒ x 2 + (x + 2) 2 = 970 ⇒ x 2 + x 2 + 4 x + 4 − 970 = 0 ⇒ 2 x 2 + 4 x − 966 = 0 ⇒ x 2 + 2 x − 483 = 0

⇒ x 2 + 23 x − 21 x − 483 = 0 ⇒ x (x + 23) − 21 (x + 23) = 0 ⇒ (x − 21) (x + 23) = 0

⇒ x − 21 = 0 or x + 23 = 0 ⇒ x = 21 or x = − 23

As integers should be positive, so x = −23 is rejected.
Therefore,

x = 21 ⇒ x + 2 = 21 + 2 ⇒ x + 2 = 23

Hence, two consecutive odd positive integers, sum of whose squares is 970 are 21 and 23
So, the correct option is 2.

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