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deathmate
 Post subject: equation with multiple absolute values
PostPosted: Thu, 8 Sep 2011 09:32:41 UTC 
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|x|+|7-x|+2|x-2|=4
and the way of solving please, cuz i have no idea :?
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aswoods
 Post subject: Re: equation with multiple absolute values
PostPosted: Thu, 8 Sep 2011 09:53:56 UTC 
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Are you sure this is the problem statement? Because there is no solution for x.
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deathmate
 Post subject: Re: equation with multiple absolute values
PostPosted: Thu, 8 Sep 2011 11:08:54 UTC 
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aswoods wrote:
Are you sure this is the problem statement? Because there is no solution for x.

yes ,this is it, and you are right , is no solution for x , but how to prove it ???step by step if you could,... :( i've stuck
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outermeasure
 Post subject: Re: equation with multiple absolute values
PostPosted: Thu, 8 Sep 2011 13:56:02 UTC 
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deathmate wrote:
|x|+|7-x|+2|x-2|=4
and the way of solving please, cuz i have no idea :?


\lvert x\rvert+\lvert 7-x\rvert\geqslant\lvert x+(7-x)\rvert=7

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\begin{aligned} Spin(1)&=O(1)=\mathbb{Z}/2&\quad&\text{and}\\ Spin(2)&=U(1)=SO(2)&&\text{are obvious}\\ Spin(3)&=Sp(1)=SU(2)&&\text{by }q\mapsto(\mathop{\mathrm{Im}}\mathbb{H}\ni p\mapsto qp\bar{q})\\ Spin(4)&=Sp(1)\times Sp(1)&&\text{by }(q_1,q_2)\mapsto(\mathbb{H}\ni p\mapsto q_1p\bar{q_2})\\ Spin(5)&=Sp(2)&&\text{by }\mathbb{HP}^1\cong S^4_{round}\hookrightarrow\mathbb{R}^5\\ Spin(6)&=SU(4)&&\text{by the irrep }\Lambda_+\mathbb{C}^4 \end{aligned}
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Shadow
 Post subject: Re: equation with multiple absolute values
PostPosted: Thu, 8 Sep 2011 19:12:29 UTC 
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outermeasure wrote:
deathmate wrote:
|x|+|7-x|+2|x-2|=4
and the way of solving please, cuz i have no idea :?


\lvert x\rvert+\lvert 7-x\rvert\geqslant\lvert x+(7-x)\rvert=7


And the triangle inequality proves once again that it is king among inequalities.

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Justin
 Post subject: Re: equation with multiple absolute values
PostPosted: Sat, 10 Sep 2011 05:50:35 UTC 
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Shadow wrote:
outermeasure wrote:
deathmate wrote:
|x|+|7-x|+2|x-2|=4
and the way of solving please, cuz i have no idea :?


\lvert x\rvert+\lvert 7-x\rvert\geqslant\lvert x+(7-x)\rvert=7


And the triangle inequality proves once again that it is king among inequalities.


LOL! Indeed, mathematical illiteracy triumphs again! :roll:

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"Mathematicians are like lovers. Grant a mathematician the least principle, and he will draw from it a consequence which you must also grant him, and from this consequence another." Bernard Le Bovier Fontenelle (1657-1757)

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