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Mathematics
Problem
If
a
,
b
a, b
a
,
b
and
c
c
c
are all different and if
∣
a
a
2
1
+
a
3
b
b
2
1
+
b
3
c
c
2
1
+
c
3
∣
=
0
,
prove that
a
b
c
=
−
1.
\begin{vmatrix} a & a^2 & 1+a^3 \\ b & b^2 & 1+b^3 \\ c & c^2 & 1+c^3 \end{vmatrix} = 0, \text{ prove that } abc = -1.
a
b
c
a
2
b
2
c
2
1
+
a
3
1
+
b
3
1
+
c
3
=
0
,
prove that
ab
c
=
−
1.
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