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2020 BMT Fall
8
BMT Algebra #8 - Inequality
BMT Algebra #8 - Inequality
Source:
October 11, 2020
Bmt
algebra
inequalities
Problem Statement
Compute the smallest value
C
C
C
such that the inequality
x
2
(
1
+
y
)
+
y
2
(
1
+
x
)
≤
(
x
4
+
4
)
(
y
4
+
4
)
+
C
x^2(1+y)+y^2(1+x)\le \sqrt{(x^4+4)(y^4+4)}+C
x
2
(
1
+
y
)
+
y
2
(
1
+
x
)
≤
(
x
4
+
4
)
(
y
4
+
4
)
+
C
holds for all real
x
x
x
and
y
y
y
.
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