Let x, y and z be positive real numbers such that x + y + z = 1. Find the minimum value of (x + y + z)/(xyz).
+1622 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.
+363 I think you made a mistake on format you wrote \(\frac{1}{(\frac{1}{3})^2}\) instead of \(\frac{1}{(\frac{1}{3})^3}\)
