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2023 Azerbaijan National Mathematical Olympiad
3
Real root of system of equations
Real root of system of equations
Source: Azerbaijan NMO 2023. Junior P3
August 24, 2023
algebra
AZE JUNIOR NATIONAL MO
Problem Statement
Find all the real roots of the system of equations:
{
x
3
+
y
3
=
19
x
2
+
y
2
+
5
x
+
5
y
+
x
y
=
12
\begin{cases} x^3+y^3=19 \\ x^2+y^2+5x+5y+xy=12 \end{cases}
{
x
3
+
y
3
=
19
x
2
+
y
2
+
5
x
+
5
y
+
x
y
=
12
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