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NZMOC Camp Selection Problems
2014 NZMOC Camp Selection Problems
7
7
Part of
2014 NZMOC Camp Selection Problems
Problems
(1)
system x^3 + y^3 = 2, kx + d = y, has no real solutions
Source: New Zealand NZMOC Camp Selection Problems 2014 p7
9/19/2021
Determine all pairs of real numbers
(
k
,
d
)
(k, d)
(
k
,
d
)
such that the system of equations
{
x
3
+
y
3
=
2
k
x
+
d
=
y
\begin{cases} x^3 + y^3 = 2 \\ kx + d = y\end{cases}
{
x
3
+
y
3
=
2
k
x
+
d
=
y
has no solutions
(
x
,
y
)
(x, y)
(
x
,
y
)
with
x
x
x
and
y
y
y
real numbers.
algebra
system of equations
System