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If x,y,z gt 0 and x + y + z = 1, the pr...

If x,y,z `gt` 0 and x + y + z = 1, the prove that
`(2x)/(1 - x) + (2y)/(1 - y) + (2z)/(1 - z) ge 3`.

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AI Generated Solution

To prove that \[ \frac{2x}{1 - x} + \frac{2y}{1 - y} + \frac{2z}{1 - z} \geq 3 \] given that \(x, y, z > 0\) and \(x + y + z = 1\), we can use the Arithmetic Mean-Harmonic Mean (AM-HM) inequality. ...
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