×

# 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
12 months ago

Sort by:

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