Find two consecutive positive even integers sum of whose squares is
40.
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Let the consecutive even integers be 2x and 2x + 2. Then,
(2x)2+(2x+2)2=340⇒8x2+8x−336=0⇒x2+x−42=0.
(x+7)(x−6)=0
The consecutive even integers are 12 and 14
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340 is one of them
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