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National and Regional Contests
India Contests
NMTC
2019 NMTC Junior
7
Simple AM-GM
Simple AM-GM
Source: NMTC Junior P7
November 2, 2019
inequalities
AM-GM
Problem Statement
The perimeter of
△
A
B
C
\triangle ABC
△
A
BC
is
2
2
2
and it's sides are
B
C
=
a
,
C
A
=
b
,
A
B
=
c
BC=a, CA=b,AB=c
BC
=
a
,
C
A
=
b
,
A
B
=
c
. Prove that
a
b
c
+
1
27
≥
a
b
+
b
c
+
c
a
−
1
≥
a
b
c
.
abc+\frac{1}{27}\ge ab+bc+ca-1\ge abc.
ab
c
+
27
1
≥
ab
+
b
c
+
c
a
−
1
≥
ab
c
.
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