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Mathematics
Mathematics
Problem
If
x
,
y
,
z
x, y, z
x
,
y
,
z
are different numbers and
Δ
=
det
(
x
x
2
1
+
x
3
y
y
2
1
+
y
3
z
z
2
1
+
z
3
)
=
0
,
\Delta = \det\!\begin{pmatrix}x & x^2 & 1+x^3 \\ y & y^2 & 1+y^3 \\ z & z^2 & 1+z^3 \end{pmatrix} = 0,
Δ
=
det
x
y
z
x
2
y
2
z
2
1
+
x
3
1
+
y
3
1
+
z
3
=
0
,
then show that
1
+
x
y
z
=
0
1 + xyz = 0
1
+
x
y
z
=
0
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