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Topic: inequalities (Read 420 times) |
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Radiohead_man
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inequalities
« on: Dec 14th, 2004, 8:28am » |
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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.
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I'm a reasonable man
get off my case, get off my case.
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JocK
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Re: inequalities
« Reply #1 on: Dec 14th, 2004, 12:41pm » |
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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
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| « Last Edit: Dec 14th, 2004, 12:44pm by JocK » |
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solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it.
xy - y = x5 - y4 - y3 = 20; x>0, y>0.
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