[TEX]S= \frac{x^2-z^2}{y+z} + \frac{y^2-x^2}{z+x} + \frac{z^2-y^2}{x+y} [/TEX]
[TEX]= x^2 . \bigg( \frac{1}{y+z} - \frac{1}{z+x} \bigg) + y^2 . \bigg( \frac{1}{z+x} - \frac{1}{x+y} \bigg) + z^2 . \bigg( \frac{1}{x+y} - \frac{1}{y+z} \bigg)[/TEX]
[TEX]= \frac{x^2(x-y)}{(y+z)(z+x)} + \frac{y^2(y-z)}{(z+x)(x+y)} + \frac{z^2(z-x)}{(x+y)(y+z)}[/TEX]
[TEX]= \frac{x^2(x^2 - y^2) + y^2(y^2 - z^2) + z^2 (z^2 - x^2)}{(x+y)(y+z)(z+x)}[/TEX]
[TEX]= \frac{(x^2 - y^2)^2 + (y^2 - z^2)^2 + (z^2 - x^2)}{2(x+y)(y+z)(z+x)}[/TEX]
[TEX]x,y,z >0 \Rightarrow A \geq 0[/TEX]
[TEX]" = " \Leftrightarrow x=y=z[/TEX]
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