MathDB
Problems
Contests
International Contests
Silk Road
2015 Silk Road
1
maybe easy but good problem
maybe easy but good problem
Source: silk road
March 9, 2016
algebra
Problem Statement
Prove that there is no positive real numbers
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
such that both of the following equations hold.
a
b
+
b
c
+
c
d
+
d
a
=
6
,
b
a
+
c
b
+
d
c
+
a
d
=
32
\frac{a}{b}+\frac{b}{c}+\frac{c}{d}+\frac{d}{a}=6 , \frac{b}{a}+\frac{c}{b}+\frac{d}{c}+\frac{a}{d}=32
b
a
+
c
b
+
d
c
+
a
d
=
6
,
a
b
+
b
c
+
c
d
+
d
a
=
32
.
Back to Problems
View on AoPS