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Polish MO Finals
1982 Polish MO Finals
3
3
Part of
1982 Polish MO Finals
Problems
(1)
x^2 +y^2 = a^2 +b^2, x^3 +y^3 = a^3 +b^3, x,y,a,b>0
Source: 1982 Polish MO Finals p3
2/25/2020
Find all pairs of positive numbers
(
x
,
y
)
(x,y)
(
x
,
y
)
which satisfy the system of equations
{
x
2
+
y
2
=
a
2
+
b
2
x
3
+
y
3
=
a
3
+
b
3
\begin{cases} x^2 +y^2 = a^2 +b^2 \\ x^3 +y^3 = a^3 +b^3 \end{cases}
{
x
2
+
y
2
=
a
2
+
b
2
x
3
+
y
3
=
a
3
+
b
3
where
a
a
a
and
b
b
b
are given positive numbers.
system of equations
parameter
algebra