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MathLinks Contest 3rd
1
0351 inequalities 3rd edition Round 5 p1
0351 inequalities 3rd edition Round 5 p1
Source:
May 9, 2021
inequalities
3rd edition
Problem Statement
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
be positive reals. Prove that
a
b
c
(
a
+
b
+
c
)
+
(
a
+
b
+
c
)
2
≥
4
3
a
b
c
(
a
+
b
+
c
)
.
\sqrt{abc}(\sqrt{a} +\sqrt{b} +\sqrt{c}) + (a + b + c)^2 \ge 4 \sqrt{3abc(a + b + c)}.
ab
c
(
a
+
b
+
c
)
+
(
a
+
b
+
c
)
2
≥
4
3
ab
c
(
a
+
b
+
c
)
.
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