A student opens a mathematics book to two facing pages. The product of the page number is 2352. Find the page numbers. Fist page number____. Second page number____.

Question

jim_thompson5910 · Answer

Let x = first page number

So x + 1 is the next page number


Multiply the two numbers and set them equal to the given product 2352


x(x+1) = 2352


Now solve for x


x(x+1) = 2352


x^2+x = 2352


x^2+x - 2352 = 0


Now use the quadratic formula to solve for x



x = (-B +- sqrt( B^2-4AC ))/(2A)


x = (-(1) +- sqrt( (1)^2-4(1)(-2352) ))/(2(1))


x = (-1 +- sqrt( 1+9408 ))/(2(1))


x = (-1 +- sqrt( 9409 ))/(2)


x = (-1 +- 97)/(2)


x = (-1 + 97)/(2) or x = (-1 - 97)/(2)


x = (96)/(2) or x =  (-98)/(2)


x = 48 or x = -49


Throw out the negative answer to get the only solution of x = 48


So the first page is 48 and the next consecutive page is 49