MathDB
Problems
Contests
National and Regional Contests
Taiwan Contests
IMOC Shortlist
2017-IMOC
A6
A6
Part of
2017-IMOC
Problems
(1)
sum sqrt(a+3b+2/c) inequality with a+b+c=3
Source: IMOC 2017 A6
8/12/2021
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
.
inequalities
algebra