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2019 District Olympiad
1
5(x^2+xy+y^2) = 7(x+2y), integer, rational 2019 Romania District VIII p1
5(x^2+xy+y^2) = 7(x+2y), integer, rational 2019 Romania District VIII p1
Source:
September 1, 2024
algebra
number theory
Problem Statement
Determine the numbers
x
,
y
x,y
x
,
y
, with
x
x
x
integer and
y
y
y
rational, for which equality holds:
5
(
x
2
+
x
y
+
y
2
)
=
7
(
x
+
2
y
)
5(x^2+xy+y^2) = 7(x+2y)
5
(
x
2
+
x
y
+
y
2
)
=
7
(
x
+
2
y
)
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