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Find the consecutive even integers whose squares have the sum 340.
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Let the consecutive even integers be 2x and 2x + 2.
Then according to the given hypothesis,
(2ЁЭСе)2 + (2ЁЭСе + 2)2 = 340
⇒ 8ЁЭСе2 + 8ЁЭСе - 336 = 0
⇒ ЁЭСе2 + ЁЭСе - 42 = 0
⇒ ЁЭСе2 + 7ЁЭСе - 6ЁЭСе - 42 = 0
⇒ ЁЭСе(ЁЭСе + 7) - 6(ЁЭСе + 7) = 0
⇒ (ЁЭСе + 7)(ЁЭСе - 6) = 0
⇒ x = -7 or x = 6
Considering, the positive integers of x.
⇒ x = 6; 2x = 12 and 2x + 2 = 14.
∴ The two consecutive even integers are 12 and 14.
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