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Contests
National and Regional Contests
Switzerland Contests
Switzerland - Final Round
2007 Switzerland - Final Round
1
1
Part of
2007 Switzerland - Final Round
Problems
(1)
6x6 system, a = max {1/b, 1/c}
Source: Switzerland - 2007 Swiss MO Final Round p1
12/26/2022
Determine all positive real solutions of the following system of equations:
a
=
m
a
x
{
1
b
,
1
c
}
b
=
max
{
1
c
,
1
d
}
c
=
max
{
1
d
,
1
e
}
a =\ max \{ \frac{1}{b} , \frac{1}{c}\} \,\,\,\,\,\, b = \max \{ \frac{1}{c} , \frac{1}{d}\} \,\,\,\,\,\, c = \max \{ \frac{1}{d}, \frac{1}{e}\}
a
=
ma
x
{
b
1
,
c
1
}
b
=
max
{
c
1
,
d
1
}
c
=
max
{
d
1
,
e
1
}
d
=
max
{
1
e
,
1
f
}
e
=
max
{
1
f
,
1
a
}
f
=
max
{
1
a
,
1
b
}
d = \max \{ \frac{1}{e} , \frac{1}{f }\} \,\,\,\,\,\, e = \max \{ \frac{1}{f} , \frac{1}{a}\} \,\,\,\,\,\, f = \max \{ \frac{1}{a} , \frac{1}{b}\}
d
=
max
{
e
1
,
f
1
}
e
=
max
{
f
1
,
a
1
}
f
=
max
{
a
1
,
b
1
}
algebra
system of equations
System
inequalities