Find the consecutive even integers whose squares have the sum 340.

Let the consecutive even integers be ‘a’ and a + 2


a2 + (a + 2)2 = 340


2a2 + 4a – 336 = 0


a2 + 2a – 168 = 0


a2 + 14a – 12a – 168 = 0


a(a + 14) – 12(a + 14) = 0


(a – 12)(a + 14) = 0


Thus, a = 12 or – 14


Consecutive even integers are 12, 14 or -14, - 12


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