If determinant ((x^n ,x^(n+2) ,x^(n+3) ),(y^n ,y^(n+2) ,y^(n+3) ),(z^n ,z^(n+2) ,z^(n+3) )) = (x−y)(y−z)(z−x)((1/x) + (1/y) + (1/z)), then n equals


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Question Number 67836 by gunawan last updated on 01/Sep/19

$If \| \begin{matrix} x^{n} & x^{n + 2} & x^{n + 3} \\ y^{n} & y^{n + 2} & y^{n + 3} \\ z^{n} & z^{n + 2} & z^{n + 3} \end{matrix} \|$ $= (x - y) (y - z) (z - x) (\frac{1}{x} + \frac{1}{y} + \frac{1}{z}),$ $then n equals$
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