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2023 JBMO Shortlist
A5
JBMO Shortlist 2023 A5
JBMO Shortlist 2023 A5
Source: JBMO Shortlist 2023, A5
June 28, 2024
inequalities
JBMO
JBMO Shortlist
algebra
AZE JBMO TST
Problem Statement
Let
a
≥
b
≥
1
≥
c
≥
0
a \geq b \geq 1 \geq c \geq 0
a
≥
b
≥
1
≥
c
≥
0
be real numbers such that
a
+
b
+
c
=
3
a+b+c=3
a
+
b
+
c
=
3
. Show that
3
(
a
b
+
b
a
)
≥
4
c
2
+
a
2
b
+
b
2
a
3 \left( \frac{a}{b}+\frac{b}{a} \right ) \geq 4c^2+\frac{a^2}{b}+\frac{b^2}{a}
3
(
b
a
+
a
b
)
≥
4
c
2
+
b
a
2
+
a
b
2
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