MathDB
Problems
Contests
National and Regional Contests
Azerbaijan Contests
Azerbaijan Junior National Olympiad
2023 Azerbaijan National Mathematical Olympiad
3
3
Part of
2023 Azerbaijan National Mathematical Olympiad
Problems
(1)
Real root of system of equations
Source: Azerbaijan NMO 2023. Junior P3
8/24/2023
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
algebra
AZE JUNIOR NATIONAL MO