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à¤Ã×èͧÁ×ͧ͢ËÑÇ¢éÍ | ¤é¹ËÒã¹ËÑÇ¢é͹Õé |
#1
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ᡵÑÇ»ÃСͺ
¢éÍ 1 (a-b)(a+b)^3 - a^4 + b^4 ________________________ ¢éÍ 2 9a^2 - b^2 - 36c^2 - 12a + 12bc + 4 ____________________ ¢éÍ3 25 - a^2 - 4b^2 + b ________________________ ¢éÍ 4 lxl^2 - 3lxl + 2 =? ________________________ ¢éÍ 5 3lx+1l^2 + 4lx+1l - 4 =? ________________________ ã¤ÃÁÕ⨷Âìà¾ÔèÁàµÔÁà¡ÕèÂǡѺ¡ÒÃᡵÑÇ»ÃСͺÃèÇÁ ¡ÒÃâÍà»ÍàêÑè¹ ¼ÅµèÒ§¡ÓÅѧ2 ¡ÓÅѧ2 ÊÁºÙÃ³ì ¢Í˹è͹ФРàÍÒÂÒ¡æ¹Ð áÅЪèǺ͡ÇÔ¸Õ¤Ô´´éǤèÐ ¢Íº¤Ø³ÁÒ¡¤èÐ ªèÇÂ˹è͹ФР´èǹàŤèШÐÊͺà¡çº¤Ðá¹¹àÃÕ¹»ÃѺ¾×é¹áÅéǤèÐ ¢Íº¤Ø³¹Ð¤Ð 20 àÁÉÒ¹ 2008 17:04 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 1 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ nongtum à˵ؼÅ: double post |
#2
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¢éÍ 1 $2ab(a-b)(a+b)$
¢éÍ 4 $(\left|\,x\right|-2)(\left|\,x\right|-1)$ ¢éÍ 5 $(3\left|\,x+1\right|-2)(\left|\,x+1\right|+2)$ |
#3
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¢éͤÇÒÁà´ÔÁ¢Í§¤Ø³ Bo_ok
ã¤ÃÁÕ⨷Âìà¾ÔèÁàµÔÁà¡ÕèÂǡѺ¡ÒÃᡵÑÇ»ÃСͺÃèÇÁ
¡ÒÃâÍà»ÍàêÑè¹ ¼ÅµèÒ§¡ÓÅѧ2 ¡ÓÅѧ2 ÊÁºÙÃ³ì ¢Í˹è͹ФРàÍÒÂÒ¡æ¹Ð áÅЪèǺ͡ÇÔ¸Õ¤Ô´´éǤèÐ ¢Íº¤Ø³ÁÒ¡¤èÐ[/quote] 1.¨§á¡µÑÇ»ÃСͺ¢Í§ $(x-y)^{3}$+$(y-z)^{3}$+$(z-x)^{3}$ |
#4
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àËç¹ä´éªÑ´ÇèÒ $(x−y) +(y−z) +(z−x) = 0$
à¾ÃÒЩйÑé¹ $(x−y)^3 +(y−z)^3 +(z−x)^3 = 3(x−y)(y−z)(z−x)$
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..The answer to everything might be 42, but where's the question? ... |
#5
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¢éÍ 2 ¢Í§¤Ø³ Bo_ok ¤ÃѺ
\[\begin{array}{rcl} 9a^2-b^2-36c^2-12a+12bc+4&=&(9a^2-12a+4)-(b^2-12bc+36c^2)\\ &=&(3a-2)^2-(b-6c)^2\\ &=&(3a-2+b-6c)(3a-2-b+6c)\\ \end{array}\]$\therefore 9a^2-b^2-36c^2-12a+12bc+4=(3a+b-6c-2)(3a-b+6c-2)$ |
#6
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àÍÒ⨷ÂìãËè¤èÐ ¡çà»ç¹â¨·Âì»Ò¹¡ÅÒ§¤èÐ áµè¡ç¹èÒʹ㨴չФÐ
1. ¨§á¡µÑÇ»ÃСͺ¢Í§ $$(a+b+c)^4-(a+b)^4-(b+c)^4-(c+a)^4+a^4+b^4+c^4$$ **¢é͹ÕéäÁè¨Óà»ç¹µéͧ¡ÃШÒ¤èÐÁͧ´Õæ¤èÐ Å᷹ͧ $P(a,b,c)=> P(a,0,0),P(0,b,0),P(0,0,c)$ áÅéǨÐä´éàͧ¤èÐ àÊÃÔÁãËéÍÕ¡¢éͤèÐ §èÒÂæ 2.)ãËé $P(x)$ à»ç¹¾ËعÒÁ´Õ¡ÃÕ 2008 «Öè§ÊÑÁ»ÃÐÊÔ·¸Ôì $x^{2008}$ à»ç¹ 1 áÅÐ $P(2007)=0,P(2006)=1,...,P(1)=2006,P(0)=2007$ áÅéǨ§ËÒ¤èҢͧ $P(2008)$ 20 àÁÉÒ¹ 2008 17:05 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 1 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ nongtum à˵ؼÅ: double post |
#7
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$$P(x)=(x)(x-1)(x-2)...(x-2007)+(2007-x)$$
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¤ Ç Ò Á ÃÑ º ¼Ô ´ ª Í º $$|I-U|\rightarrow \infty $$ |
#8
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¢Íº¤Ø³¹êÒ¤êÒ
ã¤Ãà¾ÔèÁàµÔÁÍÕ¡¡çªèÇÂá¡é ªèÇÂ͸ԺÒÂ˹è͹ФР|
#9
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ÇÔ¸Õ·Ó¢éÍ1.¹Ð¤ÃѺ
$(a-b)(a+b)^3-a^4+b^4=(a-b)(a+b)^3-(a^3-b^3)=(a-b)(a^3+3a^2b+3ab^2+b^3)-(a-b)(a^3+a^2b+ab^2+b^3)=(a-b)(2a^2b+2ab^2)=2ab(a-b)(a+b)$
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µÐ»Ù·ÕèµÍ¡º¹á¼è¹äÁé áÁé¶Í¹ÍÍ¡Âѧ¤§·Ôé§ÃÍÂäÇé ¤Ó¾Ù´·ÔèÁá·§¨Ôµã¨¤¹ ãÂÁÔãªèà»ç¹à©¡àªè¹à´ÕÂǡѹ |
#10
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¢éÍ 3. ¼Á¤Ô´ÇèÒäÁèÊÒÁÒöá¡ã¹ÃÙ»$(x_1a+x_2b+x_3)(y_1a+y_2b+y_3)$
â´Â·Õè $x_1,x_2,x_3,y_1,y_2,y_3$à»ç¹¨Ó¹Ç¹¨ÃÔ§ä´é (Íѹ¹Õé¼ÁÂѧäÁè¤èÍÂá¹è㨠áµè¼Á·ÓáÅéÇÁѹ¢Ñ´áÂ駤ÃѺ)
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µÐ»Ù·ÕèµÍ¡º¹á¼è¹äÁé áÁé¶Í¹ÍÍ¡Âѧ¤§·Ôé§ÃÍÂäÇé ¤Ó¾Ù´·ÔèÁá·§¨Ôµã¨¤¹ ãÂÁÔãªèà»ç¹à©¡àªè¹à´ÕÂǡѹ |
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