@Izzie,
ok... the whizzy lizzie prize is..... <grabs the pretend smart hat of the hatstand>
1. abs(x) = max(x, ??'x)
2. max(x, y) = ½(x + y + abs(x ??' y))
i.e.
1. By inspection, abs(x) = max(x, ??'x).
2. To express max(x, y) in terms of abs function(s), consider x and y positioned on the real number line.
The midpoint of the line is ½(x + y).
To obtain max(x, y), we then need to add half the length of the line segment connecting x and y; that is, we must add ½(abs(x ??' y)).
Hence max(x, y) = ½(x + y + abs(x ??' y)).
<Moves on... places pretend smart hat back on hatstand and returns to blonde, sasyahes out door!>
This needs to be co-sined... with verification!!!! la l al al al al alal lalll alal