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Canadian Mathematical Olympiad Qualification Repechage
2018 Canadian Mathematical Olympiad Qualification
1
A cubic system of two equations
A cubic system of two equations
Source: Canada Repêchage 2018/1
April 9, 2018
algebra
system of equations
Problem Statement
Determine all real solutions to the following system of equations:
{
y
=
4
x
3
+
12
x
2
+
12
x
+
3
x
=
4
y
3
+
12
y
2
+
12
y
+
3.
\begin{cases} y = 4x^3 + 12x^2 + 12x + 3\\ x = 4y^3 + 12y^2 + 12y + 3. \end{cases}
{
y
=
4
x
3
+
12
x
2
+
12
x
+
3
x
=
4
y
3
+
12
y
2
+
12
y
+
3.
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