if product of three numbers is 1, how do you find the minimum value of the sum of those three numbers?
i tried to find the possible values of the numbers that would give a product of one but I'm not sure if that helps in any way. I dont want the solution, i just want to know what method to use in approaching this question and how to check my answer
Added after looking at comments: The problem poser clearly intended that the three numbers all be positive.
Best Answer
Let the three numbers be $x,y,z$ and following @amcerbu replace $z = \frac{1}{xy}$. Then to find a local minimum for $$f(x,y) = x+y + \frac{1}{xy}$$ if you know calculus, you do: $$ \frac{\partial f}{\partial x} = 0 \\\frac{\partial f}{\partial y} = 0$$
Solving those equations simultaneously, you get $y^5 = 1$.