Date: Mar 8, 2013 1:08 PM
Author: clicliclic@freenet.de
Subject: can your CAS help proving inequalities?


Hello!

Let a, b, c, d be arbitrary real numbers. Define:

r(a, b, c, d) := (a - c)*(a - d)*(b - c)*(b - d)

s(a, b, c, d) := (a + b)*(c + d) - 2*(a*b + c*d) - ABS((a - b)*(c - d))

t(a, b, c, d) := (a + b)*(c + d) - 2*(a*b + c*d) + ABS((a - b)*(c - d))

Can your CAS help proving the following inequalities?

MIN(r(a, b, c, d), r(a, c, b, d), r(a, d, c, b)) <= 0

MAX(s(a, b, c, d), s(a, c, b, d), s(a, d, c, b)) >= 0

MIN(t(a, b, c, d), t(a, c, b, d), t(a, d, c, b)) <= 0

Have fun!

Martin.