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Topic: can your CAS help proving inequalities?
Replies: 19   Last Post: Mar 11, 2013 12:00 PM

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Nasser Abbasi

Posts: 5,674
Registered: 2/7/05
Re: can your CAS help proving inequalities?
Posted: Mar 8, 2013 10:04 PM
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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




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