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Tuymaada Olympiad
2016 Tuymaada Olympiad
4
Three variable inequality for juniors
Three variable inequality for juniors
Source: Tuymaada 2016. Junior League/P4
July 22, 2016
inequalities
Problem Statement
Non-negative numbers
a
a
a
,
b
b
b
,
c
c
c
satisfy
a
2
+
b
2
+
c
2
≥
3
a^2+b^2+c^2\geq 3
a
2
+
b
2
+
c
2
≥
3
. Prove the inequality
(
a
+
b
+
c
)
3
≥
9
(
a
b
+
b
c
+
c
a
)
.
(a+b+c)^3\geq 9(ab+bc+ca).
(
a
+
b
+
c
)
3
≥
9
(
ab
+
b
c
+
c
a
)
.
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