For a given iteration of the Bisection method the absolute relative approximate error is defined as

Ea $=|$xm $$ x$$m$|/$xm$,$

where x$$m is the estimate from the previous iteration. Show that

Ea $=|$xl $$ xu$|/($xl $+$ xu$),$

Hint: use a proof by cases on the case of when xl $=$ x$$m$,$ and on the case of when xu $=$ x$$m$.$