Question 132301
If we look at the page numbers, we'll notice that they are consecutive integers. So they follow the algebraic form {{{x}}}, {{{x+1}}}, {{{x+2}}}, etc.




So if the product of two consecutive integers is 1056, then we have the equation


{{{x(x+1)=1056}}}



{{{x^2+x=1056}}} Distribute



{{{x^2+x-1056=0}}} Subtract 1,056 from both sides


{{{(x+33)(x-32)=0}}} Factor the left side (note: if you need help with factoring, check out this <a href=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)




Now set each factor equal to zero:

{{{x+33=0}}} or  {{{x-32=0}}} 


{{{x=-33}}} or  {{{x=32}}}    Now solve for x in each case



So our possible solutions are
 

 {{{x=-33}}} or  {{{x=32}}} 




However, since a negative page number is not possible, this means that the only solution is {{{x=32}}}



Now to find the next page number, simply add 1 to 32 to get



{{{32+1=33}}}



So the two page numbers are 32 and 33




Check:


To check this answer, simply multiply the two numbers:



{{{32*33=1056}}}



{{{1056=1056}}} Works.