Question 720885
I hope you know some Calculus because I can;t think of any other way to solve this. If you don't know Calculus then re-post the question and say that the solution cannot use Calculus.<br>
If the two numbers are x and y, then the fact that their product is 185 would translate into:
x*y = 185
Solving for y this would give us:
y = 185/x<br>
The equation for the sum of x and y would be:
s = x + y (where "s" is the sum)
Substituting the expression we found for y gives us:
{{{s = x + 185/x}}}
To find a minimum sum we will find the first derivative...
{{{ds/dx = 1 + (-185)/x^2}}}
...set it to zero...
{{{0 = 1 + (-185)/x^2}}}
... and solve for x:
{{{x = sqrt(185)}}} or {{{x = -sqrt(185)}}}
Since x (and y) must be positive numbers, we reject the negative solution. Using {{{x = sqrt(185)}}} and solving for y gives us {{{y = sqrt(185)}}}<br>
There are various ways to check if this is a minimum and not a maximum. One way is to pick a different pair of positive numbers whose product is 185. For example, 1 and 185. The sum of these two is 186. Since {{{sqrt(185) < 14}}} the sum of two of them will be less than 28, far less than the sum of 1 and 185.<br>
So {{{x = sqrt(185)}}} and {{{y = sqrt(185)}}} does indeed represent the pair of positive