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Question Number 118023 by 1549442205PVT last updated on 14/Oct/20

$$$$$$..calculus..$$$$x,y,z\in {\mathbb{R}}^{+}and{x}^2+y^2+z^2=1$$$$$$$$find$$$${min}_{x,y,z\in {\mathbb{R}}^{+}}\left((\frac{yz}{x}+\frac{xz}{y}+\frac{xy}{z})\right)=?$$$$$$$$m.n.1970..$$

Answered by MJS_new last updated on 14/Oct/20

$$x,y,z\mathrm{symmetric}\Rightarrow x=y=z=\frac{\sqrt{3}}{3}$$$$\mathrm{answer}\mathrm{is}\sqrt{3}$$

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