Inequality

數學小子

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[a/(b+c)]+sqrt[b/(a+c)]+sqrt[c/(a+b)]>=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.

-終場ソ使者-

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 have


2

and
i.e.

so, the min. value of (x+y)(y+z) is 2.

3
since
and
so,
=>

4
since=>

天才A

belong to R+ = 口 =??
一睇到呢句
就知未教

-終場ソ使者-

belong to R+ = 口 =??
一睇到呢句
就知未教
天才A 發表於 16-10-2010 14:36

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

天才A

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

真係唔知有呢d簡寫 = =||

-終場ソ使者-

真係唔知有呢d簡寫 = =||
天才A 發表於 16-10-2010 19:48

你唔知d數學家好懶架咩-.-

天才A

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

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...

-終場ソ使者-

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

a>b=c姐係話a>b and b=c
a>c-.-

天才A

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

果3行野原來係同一行架 =口= !?