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Let x, y and z be positive real numbers such that x + y + z = 1.    Find the minimum value of (x + y + z)/(xyz).

 Jan 25, 2022
 #1
avatar+834 
+4

x + y + z = 1. Since xyz is in the denominator, we want xyz to be the largest value possible.

 

The largest value possible of xyz is only if x = y = z, so x = y = z = 1/3.

 

\(1\over{({1\over3})^2}\) = \((x + y + z)\over{xyz}\)

 

Thus, the minimum value of \((x + y + z)\over{xyz}\) is 27.

 

 

smiley

 Jan 25, 2022
 #2
avatar+361 
0

I think you made a mistake on format you wrote \(\frac{1}{(\frac{1}{3})^2}\) instead of \(\frac{1}{(\frac{1}{3})^3}\)

 Jan 26, 2022

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