Hi, 

The  of the page numbers on two facing pages of a book is 272

Let n and (n+1) represent the page numbers

 n(n+1) = 272

 n^2 + n - 272 = 0

(n+17)(n-16) = 0

       n = 16     (throwing out the negative solution for n)

Page numbers are 16 and 17

CHECKING our Answer***

 16· 17 = 272 

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