# Math Help - Find the value of determinant

1. ## Find the value of determinant

If x,y,z are all different and given that $\Rightarrow \begin{vmatrix} x & x^2 & 1+x^3 \\ y & y^2 & 1+y^3 \\ z & z^2 & 1+z^3 \end{vmatrix} =0$ Determine the value of (1+xyz).........

2. Hi,

Hint : recall (or show that) $\begin{vmatrix} 1 & x & x^2\\ 1 & y & y^2 \\ 1 & z & z^2\end{vmatrix}=(z-y)(z-x)(y-x)$.

3. Hello,
Originally Posted by Shivanand
If x,y,z are all different and given that $\Rightarrow \begin{vmatrix} x & x^2 & 1+x^3 \\ y & y^2 & 1+y^3 \\ z & z^2 & 1+z^3 \end{vmatrix} =0$ Determine the value of (1+xyz).........
Can you figure out that the determinant is $(x-y)(y-z)(z-x)(1+xyz)$ ?