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National and Regional Contests
Latvia Contests
Latvia BW TST
2018 Latvia Baltic Way TST
P2
P2
Part of
2018 Latvia Baltic Way TST
Problems
(1)
System of equations in real numbers
Source: 2018 Latvia BW TST P2
6/4/2022
Find all ordered pairs
(
x
,
y
)
(x,y)
(
x
,
y
)
of real numbers that satisfy the following system of equations:
{
y
(
x
+
y
)
2
=
2
8
y
(
x
3
−
y
3
)
=
13.
\begin{cases} y(x+y)^2=2\\ 8y(x^3-y^3) = 13. \end{cases}
{
y
(
x
+
y
)
2
=
2
8
y
(
x
3
−
y
3
)
=
13.
algebra
system of equations
algebra unsolved