Question 1059834
.
The product of two consecutive integers is 25 less than five times their sum. find the integers give your answer as 
comma separated numbers in {{{highlight(cross(acending))}}} ascending order.
~~~~~~~~~~~~~~~~~~~~~~


<pre>
Let the smaller number be "n".
Then the larger is (n+1), and the condition says

n*(n+1) = 5*(n+(n+1)) - 25.

Simplify:

{{{n^2 + n}}} = 5*(2n+1) - 25,

{{{n^2 + n}}} = 10n +5 - 25,

{{{n^2 -9n  + 20}}} = 0.

Factor

(n-4)*(n-5) = 0.

This equation has two roots n=4 and n=5.
</pre>

<U>Answer</U>.  There are two solutions and two pairs of such consecutive integers:  (4,5)  and  (5,6).