MathDB
Problems
Contests
National and Regional Contests
Turkey Contests
Turkey EGMO TST
2015 Turkey EGMO TST
1
Solve Equation (Turkey EGMO TST 2015)
Solve Equation (Turkey EGMO TST 2015)
Source: (Turkey EGMO TST 2015)
August 5, 2016
algebra
Problem Statement
a
a
a
is a real number. Find the all
(
x
,
y
)
(x,y)
(
x
,
y
)
real number pairs satisfy;
y
2
=
x
3
+
(
a
−
1
)
x
2
+
a
2
x
y^2=x^3+(a-1)x^2+a^2x
y
2
=
x
3
+
(
a
−
1
)
x
2
+
a
2
x
x
2
=
y
3
+
(
a
−
1
)
y
2
+
a
2
y
x^2=y^3+(a-1)y^2+a^2y
x
2
=
y
3
+
(
a
−
1
)
y
2
+
a
2
y
Back to Problems
View on AoPS