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Thread: Determine the value of (1+xyz)

  1. #1
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    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 $\displaystyle (1+xyz).$
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  2. #2
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by varunnayudu View Post
    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.
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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 $\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$\displaystyle \begin{vmatrix}
    1 & x & x^2 \\
    1 & y & y^2 \\
    1 & z & z^2
    \end{vmatrix} = (x-y)(y-z)(z-x)$ ?
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