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Greece Contests
Greece JBMO TST
2014 Greece JBMO TST
1
1
Part of
2014 Greece JBMO TST
Problems
(1)
system (x^{2}+y^{2})^{2}-xy(x+y)^{2}=19 and | x - y | = 1
Source: Greece JBMO TST 2014 p1
4/29/2019
Find all the pairs of real numbers
(
x
,
y
)
(x,y)
(
x
,
y
)
that are solutions of the system:
(
x
2
+
y
2
)
2
−
x
y
(
x
+
y
)
2
=
19
(x^{2}+y^{2})^{2}-xy(x+y)^{2}=19
(
x
2
+
y
2
)
2
−
x
y
(
x
+
y
)
2
=
19
∣
x
−
y
∣
=
1
| x - y | = 1
∣
x
−
y
∣
=
1
algebra
system of equations
Solve system