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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).

Guest Jan 25, 2022

proyaop · Answer 1 · 2022-01-25T07:56:17

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.

XxmathguyxX · Answer 2 · 2022-01-26T12:24:50

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