Triangle Inequality
Algebra
Level
4
\[E(x,y,z) = \dfrac {|x+y|}{|x|+|y|} + \dfrac {|y+z|}{|y|+|z|} + \dfrac {|z+x|}{|z|+|x|}\]
The above expression is defined for non-zero reals \(x, y, z\).
If the minimum value of \(E\) is \(a\) and the maximum value is \(b\), find \(a+b\).
by
Sharky Kesa