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Mathematics
Problem
The total number of distinct
x
∈
R
x \in \mathbb{R}
x
∈
R
for which
∣
x
x
2
1
+
x
3
2
x
4
x
2
1
+
8
x
3
3
x
9
x
2
1
+
27
x
3
∣
=
10
\begin{vmatrix} x & x^2 & 1+x^3 \\ 2x & 4x^2 & 1+8x^3 \\ 3x & 9x^2 & 1+27x^3 \end{vmatrix} = 10
x
2
x
3
x
x
2
4
x
2
9
x
2
1
+
x
3
1
+
8
x
3
1
+
27
x
3
=
10
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