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JOM 2015 Shortlist
A1
Inequality
Inequality
Source: Junior Olympiad of Malaysia Shortlist 2015 A1
July 17, 2015
Inequality
inequalities
Problem Statement
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
be the side lengths of a triangle. Prove that
∑
c
y
c
(
a
2
+
b
2
)
(
a
+
c
)
b
≥
2
(
a
2
+
b
2
+
c
2
)
\displaystyle\sum_{cyc} \frac{(a^2 + b^2)(a + c)}{b} \ge 2(a^2 + b^2 + c^2)
cyc
∑
b
(
a
2
+
b
2
)
(
a
+
c
)
≥
2
(
a
2
+
b
2
+
c
2
)
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