Determine two consecutive even positive integers, the sum of whose squares is 100?

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Ram Mohan Arumilli

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Let the two consecutive even numbers be ' 2 a ' and ( 2 a + 2) where, a > 0 . Since the sum of their squares=100; we get 4 a*a+ 4 ( a*a+2a+1) = 100==> 2a*a+2a+1 = 25==> 2 a*a + 2 a -24 =0 solving this, we get a = 3 and a= -4. taking only +ve value of a=3, the required numbers are '6' and '8'.
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