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JBMO TST - Turkey
2012 JBMO TST - Turkey
3
2-variable symmetric inequality
2-variable symmetric inequality
Source: Turkey JBMO Team Selection Test Problem 7
May 30, 2012
inequalities
function
inequalities proposed
Problem Statement
Show that for all real numbers
x
,
y
x, y
x
,
y
satisfying
x
+
y
≥
0
x+y \geq 0
x
+
y
≥
0
(
x
2
+
y
2
)
3
≥
32
(
x
3
+
y
3
)
(
x
y
−
x
−
y
)
(x^2+y^2)^3 \geq 32(x^3+y^3)(xy-x-y)
(
x
2
+
y
2
)
3
≥
32
(
x
3
+
y
3
)
(
x
y
−
x
−
y
)
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