Question 1097048

The difference between two positive integers is 3. If the smaller is added to the square of the larger, the sum is 107. Find the integers.
<pre>Let smaller number be S
Then larger = S + 3
We then get: {{{matrix(1,3, S + (S + 3)^2, "=", 107)}}}
{{{matrix(1,3, S + S^2 + 6S + 9, "=", 107)}}}
{{{matrix(1,3, S^2 + 7S - 98, "=", 0)}}}
(S - 7)(S + 14) = 0
Smaller number or {{{highlight_green(matrix(1,3, S, "=", 7))}}}          OR         S = - 14 (ignore)
Larger number: {{{highlight_green(matrix(1,3, 7 + 3, "=", 10))}}}