
can your CAS help proving inequalities?
Posted:
Mar 8, 2013 1:08 PM


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.

