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1988 All Soviet Union Mathematical Olympiad
480
ASU 480 All Soviet Union MO 1988 min of xy/z+yz/x+zx/y if x^2+y^2+z^2=1
ASU 480 All Soviet Union MO 1988 min of xy/z+yz/x+zx/y if x^2+y^2+z^2=1
Source:
August 8, 2019
algebra
inequalities
minimum
Problem Statement
Find the minimum value of
x
y
z
+
y
z
x
+
z
x
y
\frac{xy}{z} + \frac{yz}{x} +\frac{ zx}{y}
z
x
y
+
x
yz
+
y
z
x
for positive reals
x
,
y
,
z
x, y, z
x
,
y
,
z
with
x
2
+
y
2
+
z
2
=
1
x^2 + y^2 + z^2 = 1
x
2
+
y
2
+
z
2
=
1
.
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