The book is open at random and the product of the page numbers is 5550. Let the page number on the left page be n, which makes the page number of right page be n+1.
So, n(n+1)=5550
we can do this be completing the square:
n^{2}+n=5550
in order to complete the square, we need the square of one-half of the coefficient of the n, which is 1/4, so:
n^{2}+n+0.25=5550.25
(n+1/2)^{2}=5550.25
Take the square root of both sides and solve for n.
TTFN,
Eden