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**math****Member**- Registered: 2005-10-17
- Posts: 16

A)

I is a point in triangle ABC such that angle IBA > angle ICA , angle IBC > angle ICB , BI cut AC at B' , CI cut AB at C' . PRove the : BB' < CC'

please help me i'm very thanks

and the second problem

B)

a,b,c>0 prove the equation have 1 root :

d^3 - d(ab+bc+ca) - 2abc =0 .

from the equation and x,y,z >0 . ax+by+cz=xyz . Prove the inequality

x+y+z >= 2/d . (\sqrt[(a+d)(b+d)(c+d)])

C)in assemble N ,every number is white or black so that white + black=black

prove : white + white = white

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**math****Member**- Registered: 2005-10-17
- Posts: 16

nobody can help me !!!!!!!!

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**Zach****Member**- Registered: 2005-03-23
- Posts: 2,075

I do complex theories, such as Chaos Theory and the Butterfly Effect.

I, however, lack certain math skills.

Boy let me tell you what:

I bet you didn't know it, but I'm a fiddle player too.

And if you'd care to take a dare, I'll make a bet with you.

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**math****Member**- Registered: 2005-10-17
- Posts: 16

can you post the answer ?

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**math****Member**- Registered: 2005-10-17
- Posts: 16

please i'm very very need !!!!!!!

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,535

Hi math, and welcome to the forum.

These are tough questions! Where did they come from? I had a quick look and found I couldn't give an immediate answer ... other people might be the same, so you may have to wait, sorry.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**math****Member**- Registered: 2005-10-17
- Posts: 16

MathsIsFun wrote:

Where did they come from? I had a quick look and found I couldn't give an immediate answer

i don't understand . Why !!!!!!!!!!!!!!

are you have the answer of the problem ????

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,535

No, not yet. Proofs are very difficult.

Ideas are easy, though. For "C" I can think of:

white + black=black

therefore: black-black=white, but black-black=0

therefore: white+white = 0 + 0 = 0 = white

But this is not really a *proof*

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**math****Member**- Registered: 2005-10-17
- Posts: 16

your proff is wrong . please help me in problem B,C

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,535

Yes, that's right ... I said it wasn't really a proof.

I am sorry, but your questions are difficult, I am just hoping someone can spare the time to work on answer for you. I have unfortunately been a little busy recently.

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**math****Member**- Registered: 2005-10-17
- Posts: 16

thanks . I will be waiting for you

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**math****Member**- Registered: 2005-10-17
- Posts: 16

nobody

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**Flowers4Carlos****Member**- Registered: 2005-08-25
- Posts: 106

never fear!!! Flowers4Carlos is here to save the day!!!!

*looks at the problem*

eeeeek..... *falls down*

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,535

Maybe ganesh could post these one at a time under "Ganesh's Puzzles".

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**math****Member**- Registered: 2005-10-17
- Posts: 16

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,413

math wrote:

C)in assemble N ,every number is white or black so that white + black=black

prove : white + white = white

Let white=0, black=1;

white + black = 0 + 1 = 1 = black

white + white = 0 + 0 = 0 = white, Proved!

For A), B) please give some time. Yes, Proofs aren't too easy. They are time consuming.

Character is who you are when no one is looking.

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**math****Member**- Registered: 2005-10-17
- Posts: 16

very thanks to ganesh !!!!

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**math****Member**- Registered: 2005-10-17
- Posts: 16

next week , i will give the proof to my teacher ,please , !!!!!!!

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**math****Member**- Registered: 2005-10-17
- Posts: 16

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**math****Member**- Registered: 2005-10-17
- Posts: 16

the problem were unsolve in along time ago !!!!!!!!!

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

Draw the triangle, and then draw it again rotated so that B is in the same corner that C was. Now since ICA < IBA and ICB < IBC, ICA + ICB < IBA + IBC. Since this is true, the angle at C is less than the angle at B. I forget the name of the proof, but if you have such a triangle, the side with a greater angle has a smaller diagonal (BB' and CC'). So Since angle C < B, CC' > BB'.

I don't understand quite understand the wording in 2.

*Last edited by Ricky (2005-12-04 09:19:24)*

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

Ganesh,

I think c) proof isn't very right. Because you have "let" here. Here's a proof without "let":

(b means black, w means white)

Let...

b1+w1=b2

b2+w2=b3

so

b1+w1+w2=b3; b1+(w1+w2)=b3,

but

b1+w3=b3, so w1+w2=w3.

IPBLE: Increasing Performance By Lowering Expectations.

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