Inequality
1.Given that a,b,c belong to R+,show that(1) c/(a+b)+b/(a+c)+a/(b+c)>=3/2;
(2) sqrt+sqrt+sqrt>=2.
2.Let x,y,z belong to R+,find the min. value of (x+y)(y+z) if xyz(x+y+z)=1.
3.Let α,β belong to (0,π/2),prove that 1/cos2α+1/(sin2α cos2β sin2β)>=9.
4.Let α=/=nπ/2 (n belongs to Z), prove that (1+1/sin2nα)(1+1/cos2nα)>=(1+2n)2. 本帖最後由 -終場ソ使者- 於 16-10-2010 00:01 編輯
呢d係pure黎,你又post左係呢到-.-
其實我都好鍾意做呢D題目
1(1)
since http://upload.wikimedia.org/math/0/f/d/0fd2f881d030a2484cc922c558776742.png
http://upload.wikimedia.org/math/6/9/5/6952d3fc469f7f974fa041093436f9b2.png
http://upload.wikimedia.org/math/a/3/e/a3e426f8037f75e93576d4c3a78e1c9b.png
http://upload.wikimedia.org/math/f/a/1/fa1fc7d5b8043a8d3bb62bb1cc428119.png
http://upload.wikimedia.org/math/d/a/9/da9fb3d35a440b1733ee6df5eb86ba45.png http://upload.wikimedia.org/math/e/3/5/e3548938796b306b3cc6d7677b25ba3b.png
1(2)
http://upload.wikimedia.org/math/2/5/b/25b4b9c41ab916506673ed5d4ec800b1.png
i.e.http://upload.wikimedia.org/math/8/4/c/84c13667cb37cb74ae7cad91275f7bde.png
similarly, we have
http://upload.wikimedia.org/math/b/8/d/b8dd7d8a8ae4f4004b5f89f12531af8c.png
2
http://upload.wikimedia.org/math/7/9/c/79ce0bd007cc867edf9d3cba4aa6916b.png
and http://upload.wikimedia.org/math/8/f/8/8f82893f6f2773f29f022e9d535967ae.png
i.e.http://upload.wikimedia.org/math/1/6/d/16d938c608567f4f58104babaf6f9066.png
http://upload.wikimedia.org/math/0/6/5/0658b1ffff52580b8bfb41a7d71483d5.png
so, the min. value of (x+y)(y+z) is 2.
3
sincehttp://upload.wikimedia.org/math/b/7/6/b76b6cd14d953d7a05e0763fa517cf24.png
andhttp://upload.wikimedia.org/math/5/b/1/5b16986fc915a06dfeaa8950f3758733.png
so,http://upload.wikimedia.org/math/0/9/9/099a7d844495066608bff869207b8275.png
=>http://upload.wikimedia.org/math/0/c/4/0c414860efa5827910c8ef3465f5a89f.png
4
sincehttp://upload.wikimedia.org/math/c/5/6/c5697dbfe8b2ce72a3ebd5892f6feb9e.png=>http://upload.wikimedia.org/math/3/e/d/3edfe809286b02347dc85753bd598fff.png
http://upload.wikimedia.org/math/7/3/7/73748859d73c6247fdf0662781e089cb.png
http://upload.wikimedia.org/math/d/1/8/d1867e69d2e1c54bce0dfc4985837969.png belong to R+ = 口 =??
一睇到呢句
就知未教 belong to R+ = 口 =??
一睇到呢句
就知未教
天才A 發表於 16-10-2010 14:36 http://www4.nakuz.com/bbs/images/common/back.gif
x belongs to R+係指x係一個+ve real no.
C=complex number
R=real number
Q=rational number
Z=integer
N=natural number x belongs to R係指x係一個+ve real no.
C=complex number
R=real number
Q=rational number
Z=integer
N= ...
-終場ソ使者- 發表於 16-10-2010 19:14 http://www1.nakuz.com/bbs/images/common/back.gif
真係唔知有呢d簡寫 = =|| 真係唔知有呢d簡寫 = =||
天才A 發表於 16-10-2010 19:48 http://www4.nakuz.com/bbs/images/common/back.gif
你唔知d數學家好懶架咩-.- 呢d係pure黎,你又post左係呢到-.-
其實我都好鍾意做呢D題目
1(1)
since
1(2)
i.e.
similarly, we ha ...
-終場ソ使者- 發表於 15-10-2010 22:45 http://www1.nakuz.com/bbs/images/common/back.gif
其實個第1part最尾做到係 = 3/2 ...
= =...
但係題目唔係話要證大於或等於 3/2 咩= =?
定係後面已經包埋左... 其實個第1part最尾做到係 = 3/2 ...
= =...
但係題目唔係話要證大於或等於 3/2 咩= =?
定係後面已經包埋 ...
天才A 發表於 16-10-2010 19:54 http://www4.nakuz.com/bbs/images/common/back.gif
a>b=c姐係話a>b and b=c
a>c-.- a>b=c姐係話a>b and b=c
a>c-.-
-終場ソ使者- 發表於 16-10-2010 19:58 http://www1.nakuz.com/bbs/images/common/back.gif
果3行野原來係同一行架 =口= !?
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