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2023 JBMO TST - Turkey
1
Inequalities in Turkey JBMO TST
Inequalities in Turkey JBMO TST
Source: Turkey JBMO TST 2023 Day 2 P1
April 30, 2023
inequalities
algebra
Problem Statement
Prove that for all
a
,
b
,
c
a,b,c
a
,
b
,
c
positive real numbers
a
4
+
1
b
3
+
b
2
+
b
+
b
4
+
1
c
3
+
c
2
+
c
+
c
4
+
1
a
3
+
a
2
+
a
≥
2
\dfrac{a^4+1}{b^3+b^2+b}+\dfrac{b^4+1}{c^3+c^2+c}+\dfrac{c^4+1}{a^3+a^2+a} \ge 2
b
3
+
b
2
+
b
a
4
+
1
+
c
3
+
c
2
+
c
b
4
+
1
+
a
3
+
a
2
+
a
c
4
+
1
≥
2
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