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2019 Slovenia Team Selection Test
2
Slovenia 2019 TST1 P2
Slovenia 2019 TST1 P2
Source: 2019 Slovenia 1st TST Problem 2
February 18, 2019
TST
inequalities
Problem Statement
Prove, that for any positive real numbers
a
,
b
,
c
a, b, c
a
,
b
,
c
who satisfy
a
2
+
b
2
+
c
2
=
1
a^2+b^2+c^2=1
a
2
+
b
2
+
c
2
=
1
the following inequality holds.
1
a
−
a
+
1
b
−
b
+
1
c
−
c
≥
2
a
+
2
b
+
2
c
\sqrt{\frac{1}{a}-a}+\sqrt{\frac{1}{b}-b}+\sqrt{\frac{1}{c}-c} \geq \sqrt{2a}+\sqrt{2b}+\sqrt{2c}
a
1
−
a
+
b
1
−
b
+
c
1
−
c
≥
2
a
+
2
b
+
2
c
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