SOLUTION: A student opens a mathematics book to two facing pages. The product of the page numbers is 1190. Find the page numbers. The first page is ___________. The second page is ________

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Question 374361: A student opens a mathematics book to two facing pages. The product of the page numbers is 1190. Find the page numbers. The first page is ___________. The second page is ______________.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Call the left page p
The right page is p+%2B+1
given:
p+%2A%28+p+%2B+1%29+=+1190
p%5E2+%2B+p+=+1190
I'll complete the square to find the roots
p%5E2+%2B+p+%2B+%281%2F2%29%5E2+=+1190+%2B+%281%2F2%29%5E2
p%5E2+%2B+p+%2B+1%2F4+=+1190+%2B+1%2F4
%28p+%2B+1%2F2%29%5E2+=+%281190%2A4+%2B+1%29%2F4
%28p+%2B+1%2F2%29%5E2+=+4761%2F4
%28p+%2B+1%2F2%29%5E2+=+%2869%2F2%29%5E2
p+%2B+1%2F2+=+69%2F2
p+=+69%2F2+-+1%2F2
p+=+34
p+%2B+1+=+35
The pages are 34 and 35
check:
34%2A35+=+1190
OK