
Re: can your CAS help proving inequalities?
Posted:
Mar 8, 2013 10:04 PM


On 3/8/2013 12:08 PM, clicliclic@freenet.de wrote: > > 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. >
Would showing that the CAS found {} as solution for
MIN(r(*)...) >0
but found at least one solution for
MIN(r(*)...) <= 0
qualify?
Nasser

