Question

An ancienct manuscript is on display in a museum case. To what pages is the manusript open of the product of the page numbers is 9, 312?

Answer 1

n(n-1) = 9312
n^2 - n - 9312 = 0

n= (1/2)(1 +/- sqrt(1+37248))
n = 1/2 +/- 193/2
n = 194/2 or a negative number
n = 97
n-1 = 96
check
96*97 =

Answer 2

By the way, you could get there faster by guessing
sqrt (10,000) is 100
so it is a little under 100
try 95 and 96 --> 9120 too small
try 96 and 97 ---> 9312 score!