Question 170547
Let {{{n}}}= the 1st page number
{{{n + 1}}} will be the next page number
given:
{{{n*(n+1) = 600}}}
{{{n^2 + n = 600}}}
Complete the square by taking 1/2 of the co-efficient of {{{x}}},
square it and add it to both sides.
{{{n^2 + n + 1/4 = 600 + 1/4}}}
Note that the left side is a perfect square
{{{(n + 1/2)^2 = 2401/4}}}
Take the square root of both sides
{{{n + 1/2 = 49/2}}}
{{{n = 49/2 - 1/2}}}
{{{n = 24}}}
{{{n + 1 = 25}}}
check:
Does {{{24*25 = 600}}}?
Yes
Note that I used only the (+) square root of {{{2401/4}}}
since the (-) root is not useful