What are the two consecutives even integers whose squares have sum 340?

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12,10

-12,-14

12,14

Both 2 and 3

answer is D.

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Detailed Solution

Let the first even integer be 2x
Second even integer will be 2x + 2
According to the question,
(2x)2 + (2x + 2)2 = 340
or,4x2 + 4x2 + 4 + 8x = 340
or,8x2 + 8x – 336 = 0
or, x2 + x – 42 = 0
or,x2 + 7x – 6x – 42 = 0
or,x(x + 7) – 6(x + 7) = 0
or,(x + 7)(x – 6) = 0
or,x = -7 and x = 6
If x = -7
2x = 2 (-7) = -14
2x + 2 = 2 (-7) + 2
= -14 + 2 = -12
➔ Two consecutives terms are -14 and -12.
If x =6
2x = 2(6) = 12
2x + 2 = 2(6) + 2
= 12 + 2 = 14
➔ Two consecutives terms are 12 and 14.
Hence, Option (4) is the correct answer.

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