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Moldova Team Selection Test
2020 Moldova Team Selection Test
7
Inequality
Inequality
Source: Moldova TST 2020
March 7, 2020
Inequality
inequalities
Moldova
algebra
Problem Statement
Show that for any positive real numbers
a
a
a
,
b
b
b
,
c
c
c
the following inequality takes place
a
7
a
2
+
b
2
+
c
2
+
b
a
2
+
7
b
2
+
c
2
+
c
a
2
+
b
2
+
7
c
2
≤
1.
\frac{a}{\sqrt{7a^2+b^2+c^2}}+\frac{b}{\sqrt{a^2+7b^2+c^2}}+\frac{c}{\sqrt{a^2+b^2+7c^2}} \leq 1.
7
a
2
+
b
2
+
c
2
a
+
a
2
+
7
b
2
+
c
2
b
+
a
2
+
b
2
+
7
c
2
c
≤
1.
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