Question 84
Prove that if $x$, $y$ and $a$ are real numbers from the interval $(0,1)$, then
$$
\frac{|x-y|}{1-x y} \leq \frac{\left|x^{a}-y^{a}\right|}{1-x^{a} y^{a}}
$$
$$
\frac{|x-y|}{1-x y} \leq \frac{\left|x^{a}-y^{a}\right|}{1-x^{a} y^{a}}
$$
MathNet 2006 — Part 02 Question 84
Math Olympiad Vault · MathNet 2006 — Part 02