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2008 Cuba MO
7
a^2+a+b^2>= a^4+a^3+b^4 - 2008 Cuba MO 2.7
a^2+a+b^2>= a^4+a^3+b^4 - 2008 Cuba MO 2.7
Source:
August 27, 2024
algebra
inequalities
Problem Statement
For non negative reals
a
,
b
a,b
a
,
b
we know that
a
2
+
a
+
b
2
≥
a
4
+
a
3
+
b
4
a^2+a+b^2\ge a^4+a^3+b^4
a
2
+
a
+
b
2
≥
a
4
+
a
3
+
b
4
. Prove that
1
−
a
4
a
2
≥
b
2
−
1
b
\frac{1-a^4}{a^2}\ge \frac{b^2-1}{b}
a
2
1
−
a
4
≥
b
b
2
−
1
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