Question

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

• A. 12 and 10
• B. –12 and –14
• C. 12 and 14
• D. Both (B) and (C)

Answer 1

The correct option is D

Both (B) and (C)

Let the first even integer be 2x
Second even integer will be 2x + 2
According to the question,
(2x)² + (2x + 2)² = 340
4x² + 4x² + 4 + 8x = 340
8x² + 8x – 336 = 0
x² + x – 42 = 0
x² + 7x – 6x – 42 = 0
x(x + 7) – 6(x + 7) = 0
(x + 7)(x – 6) = 0
x = -7 and x = 6
If x = -7
2x = 2 -7 = -14
2x + 2 = 2 -7 + 2
= -14 + 2 = -12
If x =6
2x = 2 6 = 12
2x + 2 = 2 6 + 2
= 12 + 2 = 14