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#1

$Old$ November 5th, 2009, 08:53 AM

sf1903 $sf1903 is offline$

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Let x,y,z be three real numbers that are mutually different, x=y x=z y=z .

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#2

$Old$ November 5th, 2009, 09:11 AM

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This is a Vandermonde determinant and it is equal to $(z-x)(z-y)(y-x)$

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#3

$Old$ November 5th, 2009, 09:25 AM

sf1903 $sf1903 is offline$

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sorry could you be more specific?

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$Old$ November 5th, 2009, 10:19 AM

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What he is saying is "go ahead and calculate the determinant"! I don't know what methods you know for finding a determinant but it is probably simplest to "expand on the first column":
$\left|\begin{array}{ccc}1 & x & x^2 \\ 1 & y & y^2 \\ 1 & z & z^2\end{array}\right|= \left|\begin{array}{cc}y & y^2 \\z & z^2 \end{array}\right|- \left|\begin{array}{cc}x & x^2 \\z & z^2 \end{array}\right|+ \left|\begin{array}{cc}x& x^2 \\y& y^2 \end{array}\right|$ .

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