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avatar+166 

Let \(x,y,z\)  be distinct real numbers that sum to 0. Find the maximum possible value of\

\(\frac{xy+yz+zx}{x^2+y^2+z^2}.\)

 Jul 28, 2019
 #1
avatar+5798 
+3

\((x+y+z)^2 = x^2+y^2+z^2 + 2xy+2xz+2yz\\~\\ 0=\dfrac{(x+y+z)^2}{x^2+y^2+z^2}=\dfrac{2xy+2xz+2yz}{x^2+y^2+z^2}+1\\~\\ \dfrac{xy+xz+yz}{x^2+y^2+z^2}=-\dfrac 1 2\)

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 Jul 28, 2019
 #2
avatar+166 
+2

Thankyou Rom

 Jul 28, 2019

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