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Kyrgyzstan Contests
Kyrgyzstan Regional Olympiad
2017 Kyrgyzstan Regional Olympiad
3
inequality algebra
inequality algebra
Source: kYRGYZSTAN REGIONAL
March 7, 2017
inequalities
Problem Statement
If
∣
x
∣
<
1
{|x|}<{1}
∣
x
∣
<
1
and
∣
y
∣
<
1
{|y|}<1
∣
y
∣
<
1
then prove that
∣
x
−
y
1
−
x
y
∣
<
1
|\frac{x-y}{1-xy}|<1
∣
1
−
x
y
x
−
y
∣
<
1
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