a studen opens a book to two facing pages. the product of the page numbers is 1332 find the page numbers? a studen opens a book to two facing pages. the product of the page numbers is 1332 find the page numbers? @Mathematics

Question

across · Answer

This question can be reworded to something like this: "What are two consecutive numbers whose product is 1332?"

across · Answer

$$x(x+1)=1332$$$$x^2+x=1332$$$$x^2+x+\frac{1}{4}=1332+\frac{1}{4}$$$$\left ( x+\frac{1}{2} \right )^2=\frac{5329}{4}$$$$x+\frac{1}{2}=\pm\frac{73}{2}$$$$x=36,-37$$

across · Answer

You pick the page numbers. ;)

asnaseer · Answer

@Zarkon has a neat way of solving these types of problems, he just finds the factors of the product in question and "sees" the solution emerge - works on most of these types of problems.
e.g.:
$$1332=2^2*3^2*37=4*9*37=36*37$$so the page numbers are 36 and 37.