Question 1092290
.
<pre>
x - y = 24,
xy  ---->  min.


It is the same as to find the minimum of the quadratic function x*(x-24), or, which is the same, of the quadratic function {{{x^2 -24x}}}.


The roots of the function are at 0 and 24; therefore, the minimum is at  the middle point  x = {{{24/2}}} = 12.

Then y = 12-24 = -12.
</pre>

<U>Answer</U>.  The numbers are 12 and - 12.



See the plot below as an illustration.


{{{graph( 330, 330, -6.5, 30.5, -150.5, 100.5,
          x^2 - 24x
)}}}


Plot y = x*(x-24)