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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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Posts: 1,090
Registered: 4/26/08
can your CAS help proving inequalities?
Posted: Mar 8, 2013 1:08 PM
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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!


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