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        riddles >> putnam exam (pure math) >> inequalities
        
(Message started by: Radiohead_man on Dec 14th, 2004, 8:28am)
Title: inequalities
Post by Radiohead_man on Dec 14th, 2004, 8:28am
Put the numbers
x = (a + b)(c + d)
y = (a + c)(b + d)
z = (a + d)(b + c)
in ascending order, if a < b < c < d.
Title: Re: inequalities
Post by JocK on Dec 14th, 2004, 12:41pm
::[hide]
a+b < a+c < a+d
a+b < a+c < b+c
c+d > b+d > a+d
c+d > b+d > b+c

now think about rectangles with circumference twice a+b+c+d :  the more elongated the rectangle, the smaller the area
      [bigto]  x < y < z
[/hide]::


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