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Germany Contests
German National Olympiad
1996 German National Olympiad
4
\sqrt[3]{x^2 }+\sqrt[3]{xy}+\sqrt[3]{y^2} = 7, x-y = 7
\sqrt[3]{x^2 }+\sqrt[3]{xy}+\sqrt[3]{y^2} = 7, x-y = 7
Source: Germany 1996 p4
February 22, 2020
system of equations
algebra
Problem Statement
Find all pairs of real numbers
(
x
,
y
)
(x,y)
(
x
,
y
)
which satisfy the system
{
x
−
y
=
7
x
2
3
+
x
y
3
+
y
2
3
=
7
\begin{cases} x-y = 7 \\ \sqrt[3]{x^2}+\sqrt[3]{xy}+\sqrt[3]{y^2} = 7\end{cases}
{
x
−
y
=
7
3
x
2
+
3
x
y
+
3
y
2
=
7
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