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Q.

The sum of the squares of two consecutive positive odd numbers is 514. Find the numbers.


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a

13, 15

b

11, 13

c

15, 17

d

17, 19 

answer is B.

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Detailed Solution

detailed_solution_thumbnail
Given that the sum of the squares of two consecutive positive odd numbers is 514.
Let's assume that n and n+2 are the two consecutive positive odd numbers.
According to the question,
⟹n2+n+22=514
⟹n2+n2+4n+4=514
⟹2n2+4n+4-514=0
⟹2n2+4n-510=0
⟹nn+17-15n+17=0
⟹n-15n+17=0
⟹n-15=0 or n+17=0
⟹n=15 or n=-15 (not possible)
⟹n=15
∴n+2=15+2=17 Thus, the integers are 15 and 17.
Hence, option (2) is correct.
 
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