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Poland - Second Round
2012 Poland - Second Round
1
System of equations
System of equations
Source: Polish MO second round 2012
February 19, 2012
algebra unsolved
algebra
Problem Statement
a
,
b
,
c
,
d
∈
R
a,b,c,d\in\mathbb{R}
a
,
b
,
c
,
d
∈
R
, solve the system of equations:
{
a
3
+
b
=
c
b
3
+
c
=
d
c
3
+
d
=
a
d
3
+
a
=
b
\begin{cases} a^3+b=c \\ b^3+c=d \\ c^3+d=a \\ d^3+a=b \end{cases}
⎩
⎨
⎧
a
3
+
b
=
c
b
3
+
c
=
d
c
3
+
d
=
a
d
3
+
a
=
b
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