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# Inequality

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
7 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. · 7 months ago