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Algebra Difficulty 6.3 National olympiad Prove it

Given x,y,z∈R+,x+y+z=1x, y, z \in R^{+}, x+y+z=1, then
(1x−x)(1y−y)(1z−z)⩾(83)3\left(\frac{1}{x}-x\right)\left(\frac{1}{y}-y\right)\left(\frac{1}{z}-z\right) \geqslant\left(\frac{8}{3}\right)^{3}

Solution

None

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