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MathLinks Contest 6th
6.1
0661 inequality 6th edition Round 6 p1
0661 inequality 6th edition Round 6 p1
Source:
May 3, 2021
algebra
inequalities
6th edition
Problem Statement
Let
p
>
1
p > 1
p
>
1
and let
a
,
b
,
c
,
d
a, b, c, d
a
,
b
,
c
,
d
be positive numbers such that
(
a
+
b
+
c
+
d
)
(
1
a
+
1
b
+
1
c
+
1
d
)
=
16
p
2
.
(a + b + c + d) \left( \frac{1}{a}+\frac{1}{b}+\frac{1}{c}+\frac{1}{d}\right)= 16p^2.
(
a
+
b
+
c
+
d
)
(
a
1
+
b
1
+
c
1
+
d
1
)
=
16
p
2
.
Find all values of the ratio
R
=
max
{
a
,
b
,
c
,
d
}
min
{
a
,
b
,
c
,
d
}
R =\frac{\max \{a, b, c, d\}}{\min \{a, b, c, d\}}
R
=
m
i
n
{
a
,
b
,
c
,
d
}
m
a
x
{
a
,
b
,
c
,
d
}
(depending on the parameter
p
p
p
)
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