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2017-IMOC
A6
sum sqrt(a+3b+2/c) inequality with a+b+c=3
sum sqrt(a+3b+2/c) inequality with a+b+c=3
Source: IMOC 2017 A6
August 12, 2021
inequalities
algebra
Problem Statement
Show that for all positive reals
a
,
b
,
c
a,b,c
a
,
b
,
c
with
a
+
b
+
c
=
3
a+b+c=3
a
+
b
+
c
=
3
,
∑
cyc
a
+
3
b
+
2
c
≥
3
6
.
\sum_{\text{cyc}}\sqrt{a+3b+\frac2c}\ge3\sqrt6.
cyc
∑
a
+
3
b
+
c
2
≥
3
6
.
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