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The sum of the squares of two consecutive multiples of 7 is 637. Find the multiples.

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18,32

14,21

16,47

14,47

answer is B.

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Detailed Solution

Given,
The sum of the squares of two consecutives multiple of 7 is 637.
Assume that the first and second multiple of 7 be 7x and 7x+7 respectively.

⇒ (7 x) 2 + (7 x + 7) = 637 ⇒ 49 x 2 + 49 x 2 + 98 x + 49 = 637 ⇒ 98 x 2 + 98 x + 49 − 637 = 0 ⇒ 98 x 2 + 98 x − 588 = 0

Divide by 98,

⇒ x 2 + x − 6 = 0 ⇒ x 2 + 3 x − 2 x − 6 = 0 ⇒ x (x + 3) − 2 (x + 3) = 0 ⇒ (x + 3) (x − 2) = 0

⇒

x+3=0 or x-2=0

⇒

x=-3,2
Substitute x = 2 in our assumed first and second multiples of 7.

⇒ 7 x ⇒ 7 (2)

First multiple of 7

= 14

Second multiple,

⇒ 7 x + 7 ⇒ 7 (2) + 7

Second multiple of 7

= 21

Thus, the multiples of 7 whose sum of squares is 637 are 14 and 21 and the correct option is 2.

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