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All-Russian Olympiad
1972 All Soviet Union Mathematical Olympiad
169
169
Part of
1972 All Soviet Union Mathematical Olympiad
Problems
(1)
ASU 169 All Soviet Union MO 1972 min of least of {x, (y+ 1/x), 1/y}, for x,y>0
Source:
7/3/2019
Let
x
,
y
x,y
x
,
y
be positive numbers,
s
s
s
-- the least of
{
x
,
(
y
+
1
/
x
)
,
1
/
y
}
\{ x, (y+ 1/x), 1/y\}
{
x
,
(
y
+
1/
x
)
,
1/
y
}
What is the greatest possible value of
s
s
s
? To what
x
x
x
and
y
y
y
does it correspond?
inequalities
algebra
minimum
maximum