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MathLinks Contest 5th
2.3
0523 inequalities 5th edition Round 2 p3
0523 inequalities 5th edition Round 2 p3
Source:
May 6, 2021
inequalities
algebra
5th edition
Problem Statement
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
be positive numbers such that
a
b
c
≤
8
abc \le 8
ab
c
≤
8
. Prove that
1
a
2
−
a
+
1
+
1
b
2
−
b
+
1
+
+
1
c
2
−
c
+
1
≥
1
\frac{1}{a^2 - a + 1} +\frac{1}{b^2 - b + 1}++\frac{1}{c^2 - c + 1} \ge 1
a
2
−
a
+
1
1
+
b
2
−
b
+
1
1
+
+
c
2
−
c
+
1
1
≥
1
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