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2015 BMT Spring
17
2015 BMT Team 17
2015 BMT Team 17
Source:
January 6, 2022
algebra
Problem Statement
There exist real numbers
x
x
x
and
y
y
y
such that
x
(
a
3
+
b
3
+
c
3
)
+
3
y
a
b
c
≥
(
x
+
y
)
(
a
2
b
+
b
2
c
+
c
2
a
)
x(a^3 + b^3 + c^3) + 3yabc \ge (x + y)(a^2b + b^2c + c^2a)
x
(
a
3
+
b
3
+
c
3
)
+
3
y
ab
c
≥
(
x
+
y
)
(
a
2
b
+
b
2
c
+
c
2
a
)
holds for all positive real numbers
a
,
b
a, b
a
,
b
, and
c
c
c
. Determine the smallest possible value of
x
/
y
x/y
x
/
y
. .
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