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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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nobody can help me !!!!!!!!
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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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can you post the answer ?
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please i'm very very need !!!!!!!
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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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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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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
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
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your proff is wrong . please help me in problem B,C
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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.
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
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thanks . I will be waiting for you
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nobody
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never fear!!! Flowers4Carlos is here to save the day!!!!
*looks at the problem*
eeeeek..... *falls down*
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Maybe ganesh could post these one at a time under "Ganesh's Puzzles".
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
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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.
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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very thanks to ganesh !!!!
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next week , i will give the proof to my teacher ,please , !!!!!!!
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the problem were unsolve in along time ago !!!!!!!!!
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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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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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