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1989 All Soviet Union Mathematical Olympiad
507
ASU 507 All Soviet Union MO 1989 min of (x+y)(y+z) when (x+y+z)xyz=1, x,y,z>0
ASU 507 All Soviet Union MO 1989 min of (x+y)(y+z) when (x+y+z)xyz=1, x,y,z>0
Source:
August 14, 2019
inequalities
algebra
minimum
Problem Statement
Find the least possible value of
(
x
+
y
)
(
y
+
z
)
(x + y)(y + z)
(
x
+
y
)
(
y
+
z
)
for positive reals satisfying
(
x
+
y
+
z
)
x
y
z
=
1
(x + y + z) xyz = 1
(
x
+
y
+
z
)
x
yz
=
1
.
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