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# need help

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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
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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.

Jan 25, 2022
#2
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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