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Poland Contests
Poland - Second Round
2011 Poland - Second Round
1
System of equations
System of equations
Source: Polish MO second round 2011
February 19, 2012
algebra unsolved
algebra
Problem Statement
For
x
,
y
∈
R
x,y\in\mathbb{R}
x
,
y
∈
R
, solve the system of equations
{
(
x
−
y
)
(
x
3
+
y
3
)
=
7
(
x
+
y
)
(
x
3
−
y
3
)
=
3
\begin{cases} (x-y)(x^3+y^3)=7 \\ (x+y)(x^3-y^3)=3 \end{cases}
{
(
x
−
y
)
(
x
3
+
y
3
)
=
7
(
x
+
y
)
(
x
3
−
y
3
)
=
3
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