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2005 Slovenia National Olympiad
Problem 1
x^3-y^3=7(x-y) and x^3+y^3=5(x+y)
x^3-y^3=7(x-y) and x^3+y^3=5(x+y)
Source: Slovenia National MO 2005 2nd Grade P1
April 5, 2021
algebra
system of equations
Problem Statement
Find all real numbers
x
,
y
x,y
x
,
y
such that
x
3
−
y
3
=
7
(
x
−
y
)
x^3-y^3=7(x-y)
x
3
−
y
3
=
7
(
x
−
y
)
and
x
3
+
y
3
=
5
(
x
+
y
)
x^3+y^3=5(x+y)
x
3
+
y
3
=
5
(
x
+
y
)
.
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