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Math Help - Determine the value of (1+xyz)

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

    If x,y,z are all different and given that

     <br />
\begin{vmatrix}<br />
x & x^2 & 1+x^3 \\<br />
y & y^2 & 1+y^3 \\<br />
z & z^2 & 1+z^3<br />
\end{vmatrix} = 0<br />

    Determine the value of (1+xyz).
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  2. #2
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by varunnayudu View Post
    If x,y,z are all different and given that

     <br />
\begin{vmatrix}<br />
x & x^2 & 1+x^3 \\<br />
y & y^2 & 1+y^3 \\<br />
z & z^2 & 1+z^3<br />
\end{vmatrix} = 0<br />

    Determine the value of (1+xyz).
    it will be good if you will give some of your initial computations.
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  3. #3
    Lord of certain Rings
    Isomorphism's Avatar
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    Quote Originally Posted by varunnayudu View Post
    If x,y,z are all different and given that

     <br />
\begin{vmatrix}<br />
x & x^2 & 1+x^3 \\<br />
y & y^2 & 1+y^3 \\<br />
z & z^2 & 1+z^3<br />
\end{vmatrix} = 0<br />

    Determine the value of (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   \begin{vmatrix}<br />
1 & x & x^2  \\<br />
1 & y & y^2  \\<br />
1 & z & z^2<br />
\end{vmatrix} = (x-y)(y-z)(z-x) ?
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