有关于不等式的问题

Allen0607 · 发表于 2011-5-2 21:59:40

以前记得有个公式，但是很模糊了。比如R/（M+N）>M/(R+N)
是不是可以上下同时加上分母，然后不等式仍然成立？

Allen0607 · 发表于 2011-5-2 22:00:10

补充：或者上下同时加上分子？

sdcar2010 · 发表于 2011-5-2 22:10:35

a/b > c/d

Is a/(a+b) > c/(c+d) ? Yes.

Why?

Since a/b > c/d,
then b/a < d/c
So b/a +1 < d/c +1
So (b+a)/a < (d+c)/c
So a/(a+b) > c/(c+d)

wxch · 发表于 2011-5-3 09:16:14

a/b > c/d

Is a/(a+b) > c/(c+d) ? Yes.

Why?

Since a/b > c/d,
then b/a < d/c
So b/a +1 < d/c +1
So (b+a)/a < (d+c)/c
So a/(a+b) > c/(c+d)

-- by 会员 sdcar2010 (2011/5/2 22:10:35)

难道不用考虑政正负号吗

sdcar2010 · 发表于 2011-5-3 10:16:16

No, because no multiplication is involved.

红红的云 · 发表于 2011-5-3 10:48:47

a/b > c/d

Is a/(a+b) > c/(c+d) ? Yes.

Why?

Since a/b > c/d,
then b/a < d/c
So b/a +1 < d/c +1
So (b+a)/a < (d+c)/c
So a/(a+b) > c/(c+d)

-- by 会员 sdcar2010 (2011/5/2 22:10:35)

Since a/b > c/d,
then b/a < d/c ????
1/2>-1/3

2<-3 ?

sdcar2010 · 发表于 2011-5-3 10:56:28

Oops.

Whatever.

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