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Baltic Way
2021 Baltic Way
2
Trivial inequality from bw21
Trivial inequality from bw21
Source: Baltic Way 2021, Problem 2
November 15, 2021
inequalities
algebra
algebra proposed
Problem Statement
Let
a
a
a
,
b
b
b
,
c
c
c
be the side lengths of a triangle. Prove that
(
a
2
+
b
c
)
(
b
2
+
c
a
)
(
c
2
+
a
b
)
3
>
a
2
+
b
2
+
c
2
2
.
\sqrt[3]{(a^2+bc)(b^2+ca)(c^2+ab)} > \frac{a^2+b^2+c^2}{2}.
3
(
a
2
+
b
c
)
(
b
2
+
c
a
)
(
c
2
+
ab
)
>
2
a
2
+
b
2
+
c
2
.
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