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If \(x,y\) and \(z\) are positive proper fractions satisfying \(x+y+z=2\), prove that \[ \dfrac x{1-x} \cdot \dfrac y{1-y} \cdot \dfrac z{1-z} \ge 8 . \]

Note by Aniket Sen
12 months ago

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Substitute \(a=1-x,b=1-y,c=1-z\). Simplify the inequality and you find that it is true by AM-HM inequality. Brilliant Member · 12 months ago

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