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IMO Longlists
1987 IMO Longlists
26
26
Part of
1987 IMO Longlists
Problems
(1)
Inequality with x^2+y^2+z^2=2
Source:
9/5/2010
Prove that if
x
,
y
,
z
x, y, z
x
,
y
,
z
are real numbers such that
x
2
+
y
2
+
z
2
=
2
x^2+y^2+z^2 = 2
x
2
+
y
2
+
z
2
=
2
, then
x
+
y
+
z
≤
x
y
z
+
2.
x + y + z \leq xyz + 2.
x
+
y
+
z
≤
x
yz
+
2.
inequalities
algebra