MathDB
Problems
Contests
National and Regional Contests
Latvia Contests
Latvia BW TST
2022 Latvia Baltic Way TST
P1
P1
Part of
2022 Latvia Baltic Way TST
Problems
(1)
System of equations with powers
Source: Latvian TST for Baltic Way 2022 P1
10/25/2022
Find all triplets of positive real numbers
(
x
,
y
,
z
)
(x,y,z)
(
x
,
y
,
z
)
that satisfy the following system of equations:
{
x
+
y
2
+
z
3
=
3
y
+
z
2
+
x
3
=
3
z
+
x
2
+
y
3
=
3.
\begin{cases} x+y^2+z^3=3\\ y+z^2+x^3=3\\ z+x^2+y^3=3. \end{cases}
⎩
⎨
⎧
x
+
y
2
+
z
3
=
3
y
+
z
2
+
x
3
=
3
z
+
x
2
+
y
3
=
3.
algebra
system of equations