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Assam Mathematics Olympiad
2023 Assam Mathematics Olympiad
10
10
Part of
2023 Assam Mathematics Olympiad
Problems
(1)
Assam Mathematics Olympiad 2023 Category III Q10
Source:
9/11/2024
If
a
,
b
,
c
≠
0
a,b,c \neq 0
a
,
b
,
c
=
0
, prove that
a
2
+
b
2
c
2
+
b
2
+
c
2
a
2
+
c
2
+
a
2
b
2
≥
6
\frac{a^2+b^2}{c^2} +\frac{b^2+c^2}{a^2} +\frac{c^2+a^2}{b^2} \geq 6
c
2
a
2
+
b
2
+
a
2
b
2
+
c
2
+
b
2
c
2
+
a
2
≥
6
.