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Question
Find two consecutive positive even integers whose squares have the sum 340.
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Solution
Let two consecutive positive even integers be 2x, 2x + 2
∴ (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 = 0 or x - 6 = 0
⇒ x = -7 or x = 6
Negative integer is not required, therefore, x = 6.
Hence, integers are 6 x 2, (6 x 2)+ 2.
i.e., 12 and 14.
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