Find two consecutive even integers such that the square of the second,

decreased by twice the first, is 52.

Let the smaller even integer be N. Then the next consecutive even 

integer to N is N+2

>>...the square of the second, decreased by twice the first, is 52...<<

Translation: (N + 2)2 - 2N = 52

             (N + 2)2 - 2N = 52

               N2 + 4N + 4 = 2N + 52

              N2 + 2N - 48 = 0

            (N + 8)(N - 6) = 0 

             N + 8 = 0, so N = -8

             N - 6 = 0, so N = 6

So the integers, N and N+2, are either -8 amd -6, or 6 and 8

Edwin

  

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