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Austrian-Polish
1992 Austrian-Polish Competition
3
2\sqrt{bc + ca + ab} <= \sqrt{3} \sqrt[3]{(b + c)(c + a)(a + b)}
2\sqrt{bc + ca + ab} <= \sqrt{3} \sqrt[3]{(b + c)(c + a)(a + b)}
Source: Austrian - Polish 1992 APMC
May 7, 2020
inequalities
algebra
Problem Statement
For all positive numbers
a
,
b
,
c
a, b, c
a
,
b
,
c
prove the inequality
2
b
c
+
c
a
+
a
b
≤
3
(
b
+
c
)
(
c
+
a
)
(
a
+
b
)
3
2\sqrt{bc + ca + ab} \le \sqrt{3} \sqrt[3]{(b + c)(c + a)(a + b)}
2
b
c
+
c
a
+
ab
≤
3
3
(
b
+
c
)
(
c
+
a
)
(
a
+
b
)
.
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