# Thread: Determine the value of (1+xyz)

1. ## Determine the value of (1+xyz)

If $\displaystyle x,y,z$are all different and given that

$\displaystyle \begin{vmatrix} x & x^2 & 1+x^3 \\ y & y^2 & 1+y^3 \\ z & z^2 & 1+z^3 \end{vmatrix} = 0$

Determine the value of $\displaystyle (1+xyz).$

2. Originally Posted by varunnayudu
If $\displaystyle x,y,z$are all different and given that

$\displaystyle \begin{vmatrix} x & x^2 & 1+x^3 \\ y & y^2 & 1+y^3 \\ z & z^2 & 1+z^3 \end{vmatrix} = 0$

Determine the value of $\displaystyle (1+xyz).$
it will be good if you will give some of your initial computations.

3. Originally Posted by varunnayudu
If $\displaystyle x,y,z$are all different and given that

$\displaystyle \begin{vmatrix} x & x^2 & 1+x^3 \\ y & y^2 & 1+y^3 \\ z & z^2 & 1+z^3 \end{vmatrix} = 0$

Determine the value of $\displaystyle (1+xyz).$
Do you know that if A and B are matrices such that they differ in one row or column, then det(A + B) = det(A) + det(B) ?

Also do you know that$\displaystyle \begin{vmatrix} 1 & x & x^2 \\ 1 & y & y^2 \\ 1 & z & z^2 \end{vmatrix} = (x-y)(y-z)(z-x)$ ?