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National and Regional Contests
Kyrgyzstan Contests
Kyrgyzstan Regional Olympiad
2017 Kyrgyzstan Regional Olympiad
3
3
Part of
2017 Kyrgyzstan Regional Olympiad
Problems
(1)
inequality algebra
Source: kYRGYZSTAN REGIONAL
3/7/2017
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
inequalities