Let \(x,y,z\) be distinct real numbers that sum to 0. Find the maximum possible value of\
\(\frac{xy+yz+zx}{x^2+y^2+z^2}.\)
\((x+y+z)^2 = x^2+y^2+z^2 + 2xy+2xz+2yz\\~\\ 0=\dfrac{(x+y+z)^2}{x^2+y^2+z^2}=\dfrac{2xy+2xz+2yz}{x^2+y^2+z^2}+1\\~\\ \dfrac{xy+xz+yz}{x^2+y^2+z^2}=-\dfrac 1 2\)
Thankyou Rom
+170 
