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3
x+y+z \leq 2 +xyz
x+y+z \leq 2 +xyz
Source: Problem 6, Polish NO 1991
October 1, 2005
inequalities
three variable inequality
algebra
Problem Statement
If
x
,
y
,
z
x, y, z
x
,
y
,
z
are real numbers satisfying
x
2
+
y
2
+
z
2
=
2
x^2 +y^2 +z^2 = 2
x
2
+
y
2
+
z
2
=
2
, prove the inequality
x
+
y
+
z
≤
2
+
x
y
z
x + y + z \leq 2 + xyz
x
+
y
+
z
≤
2
+
x
yz
When does equality occur?
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