The product of two consecutive even integers is 1088. What are the numbers?

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Answer 1 · 2016-06-27T01:13:20

#{-34, -32}# or #{32, 34}#

Let #n# be the lesser of the two consecutive even integers. Then #n+2# is the greater, and

#n(n+2) = 1088#

#=> n^2+2n = 1088#

#=> n^2+2n -1088 = 0#

If we attempt to factor by grouping , we find

#(n-32)(n+34) = 0#

#=> n-32 = 0 or n+34 = 0#

#=> n = 32 or n = -34#

Thus, we have two pairs of consecutive even integers which fulfill the criteria: #{-34, -32}# or #{32, 34}#