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Find the smallest possible value of

\(\frac{(y-x)^2}{(y-z)(z-x)} + \frac{(z-y)^2}{(z-x)(x-y)} + \frac{(x-z)^2}{(x-y)(y-z)},\)

where x, y and z are distinct real numbers.

 Mar 14, 2020
 #1
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The minimum vaue is 3.

 Mar 16, 2020

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