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à¤Ã×èͧÁ×ͧ͢ËÑÇ¢éÍ | ¤é¹ËÒã¹ËÑÇ¢é͹Õé |
#1
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¡ÒÃᡵÑÇ»ÃСͺ¾ËعÒÁ
a^2+(m+n)a+mn c^2-36 p^2+2pq+q^2
m^2-n^2 a^2-4 a^4+a^2-2 3x^2-12 6m^2+29m+33 x^6-125y^3 *x^2(m-1) -5x^(m-1) +6 7a^2-12a-27 m^2+2mn+n^2 1-a^2 b^4 x^2+4x-221 (5a+2b)^2 - (3a-7b)^2 c^6-7c^3-8 x^8-16y^8 3ac-ad-3bc+bd 16m^3n+28m^2 n^2-30mn^3 x^2 -1/x a^4+64 ·Ø¡¢éÍá¡â´ÂÇÔ¸Õ¡ÓÅѧÊͧÊÁºÙóìáÅÐáÊ´§ÇÔ¸Õ·ÓÍÂèÒ§ÅÐàÍÕ´ |
#2
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$x^2+(a+b)x+ab=(x+b)(x+a)$
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âÅ¡¹ÕéÁÕ¤¹ÍÂÙè 10 »ÃÐàÀ· ¤×Í ¤¹·Õèà¢éÒã¨àÅ¢°Ò¹Êͧ áÅФ¹·ÕèäÁèà¢éÒ㨠16 µØÅÒ¤Á 2006 10:03 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 1 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ Mastermander |
#3
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¨Ð¶ÒÁ·Ñé§·Õ ËÒ¡¾ÔÁ¾ìãË餹·ÕèÍÂÒ¡¨ÐµÍºÍèÒ¹§èÒ¡ÇèÒ¹ÕéÊÑ¡¹Ô´¨Ð´Õ¤ÃѺ ¤Ô´ÇèÒ¹èÒ¨Ðà»ç¹ÁÒµÑé§áµè¨Ò¡ÇÔªÒ¡ÒÃ.¤ÍÁáÅéÇ
¼Áá¡é¡ÒþÔÁ¾ìãËéÍèÒ¹§èÒ¢Öé¹ Êèǹ·ÕèàËÅ×ÍÅͧ¤Ô´àͧ´Ù ⨷Âì¾Ç¡¹ÕéäÁèÂÒ¡ËÒ¡¾ÂÒÂÒÁ¤Ô´ÊÑ¡¹Ô´ äÁèä´éµÃ§ä˹â»Ã´¶ÒÁà¨ÒÐà»ç¹¨Ø´æ¤ÃѺ ÍÂèÒ¶ÒÁ¡ÇҴẺ¹Õé ÍéÒ§ÍÔ§:
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¤¹ä·ÂÃèÇÁã¨ÍÂèÒãªéÀÒÉÒÇÔºÑµÔ ½Ö¡¾ÔÁ¾ìÊÑÅѡɳìÊÑ¡¹Ô´ ªÕÇÔµ(¤¹µÍºáÅФ¹¶ÒÁ)¨Ð§èÒ¢Öé¹àÂÍÐ (¨ÃÔ§æ¹Ð) Stay Hungry. Stay Foolish. |
#4
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¢éÍ1,3,6,9,10,12,15,17,18 á¡äÁè¶Ù¡
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#5
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¼ÁäÁèä´éᡵÑÇ»ÃСͺàÅÂÊÑ¡¢éÍ¹Ò á¤è¾ÔÁ¾ì⨷ÂìãËéãËÁèµÒÁ·Õèá¡ÐÍÍ¡à·èÒ¹Ñé¹ ¼Ô´µÃ§ä˹¡çºÍ¡ãËéªÑ´æÊÔ¤ÃѺ
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¤¹ä·ÂÃèÇÁã¨ÍÂèÒãªéÀÒÉÒÇÔºÑµÔ ½Ö¡¾ÔÁ¾ìÊÑÅѡɳìÊÑ¡¹Ô´ ªÕÇÔµ(¤¹µÍºáÅФ¹¶ÒÁ)¨Ð§èÒ¢Öé¹àÂÍÐ (¨ÃÔ§æ¹Ð) Stay Hungry. Stay Foolish. |
#6
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#7
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Î×Á ¢éÍ1 ¹ÕéÁÕÊÁºÑµÔ¡ÒÃᨡᨧãªèäËÁ¤ÃѺ a^2 +(m+n)a+mn = a^2 +ma+na+mn
áÅéÇ·Ó¶Ù¡äËÁ¶éÒ¼Ô´µéͧ¢Íâ·É´éǤس nongtum áµè·ÓäÁ¶Ö§ä´é (a+m)( a+n) ¢éÍ2 (c-6)(c+6)áµè·ÓẺ¡ÓÅѧÊͧÊÁºÙóìäÁèà»ç¹ ¢éÍ3 ÍÂÙèã¹ÃÙ»¡ÓÅѧÊͧÊÁºÙóì àÍêÐ àËÁ×͹¢éÍ1 àÅÂÍëÍ ¤Ø³ nongtum ¤ÃѺ ¢éÍ1 Áѹ¡çÍÂÙèã¹ÃÙ»à´ÕÂǡѺ¢éÍ1ãªèäËÁ¤ÃѺ ¢éÍ4 áʹ§èÒÂáµè·ÓẺ¡ÓÅѧÊͧÊÁºÙóìäÁèà»ç¹ ¢é͹ÕéµÍº (m-n)(m+n) ¢éÍÍ×è¹æ´Ù§èÒÂáÅéÇ áµè¢éÍ10 ¼Áä¢äÁèÍÍ¡ªèÇ·դÃѺ |
#8
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¢ÍµÍºá·Ã¡ã¹¤Ó¶ÒÁÅСѹ¹Ð...
ÍéÒ§ÍÔ§:
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¤¹ä·ÂÃèÇÁã¨ÍÂèÒãªéÀÒÉÒÇÔºÑµÔ ½Ö¡¾ÔÁ¾ìÊÑÅѡɳìÊÑ¡¹Ô´ ªÕÇÔµ(¤¹µÍºáÅФ¹¶ÒÁ)¨Ð§èÒ¢Öé¹àÂÍÐ (¨ÃÔ§æ¹Ð) Stay Hungry. Stay Foolish. |
#9
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Î×Á ¤Ø³nongtum µÍºªéÒäÁèà»ç¹ËÃÍ¡¤ÃѺ¼ÁÃÍä´éáÅмÁà¢éÒàÇ纺ÍÃì´¹Õé·Ø¡àªéÒ¤ÃѺ Êèǹ¢éÍ10 ¼Áä´é·ÓáÅéǹÑ蹤×Í´Ö§µÑÇ x^m-1 ¨Ðä´é x^m-1 (x^2 -5x + 6/ x^m-1) ãªèäËÁ¶éÒ¼Ô´¡çªèÇÂá¡éËÃ×ÍãºéãËé¼Á¡çä´é
áÅÐÁÕÍÂÙè¢éÍ˹Öè§ x^2 -1/x ·ÓÂѧ䧪èÇ·դÃѺ¤Ø³ nongtum |
#10
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ÊÓËÃѺ $ x^2-\frac{1}{x} $ ·Õè¤Ø³¤³ÔµÈÒʵÃì¶ÒÁäÇé ÅͧãªéÊٵüŵèÒ§¡ÓÅѧÊÒÁ´ÙÊÔ¤ÃѺ
$ x^2-\frac{1}{x} = \frac{x^3-1}{x}=\frac{(x-1)(x^2+x+1)}{x}=(x-1)(x+1+\frac{1}{x})$ ¢ÍµÍº¢éÍÊØ´·éÒ´éÇÂáÅéǡѹ¹Ð¤ÃѺ $ a^4+64= (a^2+8)^2 -16a^2= (a^2+8)^2- (4a)^2 =(a^2-4a+8)(a^2+4a+8) $ Note : ÊÓËÃѺ¢éÍÊØ´·éÒ¹Õé ¹Óä»ÊÙèÃٻẺ·ÑèÇä»ä´éÇèÒ $ x^4+4y^4=(x^2-2xy+2y^2)(x^2+2xy+2y^2) $ ËÃ×Í·ÕèàÃÕ¡ÇèÒ Sophie Germain's identity (·Õè¤Ø³ nooonuii à¤Â͸ԺÒÂäÇé·Õè¹Õè¤ÃѺ)
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à¡ÉÕ³µÑÇàͧ »ÅÒÂÁԶعÒ¹ 2557 áµè¨Ð¡ÅѺÁÒà»ç¹¤ÃÑ駤ÃÒÇ |
#11
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àÍÒ§Õé ¼Á·Ó¢éÍ 10 ãËé´ÙàÅ´աÇèÒ
ÊÁÁµÔãËé $y=x^{m+1}$ à¢Õ¹⨷ÂìãËÁè¨Ðä´é $y^2-5y+6=(y-3)(y-2)$ áÅéÇá·¹¤èÒ¡ÅѺ¨Ðä´é $(x^{m+1}-3)(x^{m+1}-2)$ ÊèǹÍÕ¡¢éÍÃÇÁàÈÉÊèǹ¡è͹ᡵÑÇ»ÃСͺµÑÇàÈɤÃѺ
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¤¹ä·ÂÃèÇÁã¨ÍÂèÒãªéÀÒÉÒÇÔºÑµÔ ½Ö¡¾ÔÁ¾ìÊÑÅѡɳìÊÑ¡¹Ô´ ªÕÇÔµ(¤¹µÍºáÅФ¹¶ÒÁ)¨Ð§èÒ¢Öé¹àÂÍÐ (¨ÃÔ§æ¹Ð) Stay Hungry. Stay Foolish. |
#12
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¤×ͪèÇÂáÊ´§ÇÔ¸Õ¤Ô´¢éÍ4 ·Õè a^4-a^2-2 = (a^2+a+Ö[/o]2)(a^2+a-Ö[o]2)
ËÃ×Íà»ÅèÒ¤ÃѺ |
#13
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¢éÍÊÕèá¡ÂѧäÁè¶Ù¡¤ÃѺ ãºéÇèÒ $(x-1)(x+1)$ à»ç¹µÑÇ»ÃСͺ¤ÃѺ ·ÕèàËÅ×ÍËÒàͧ
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¤¹ä·ÂÃèÇÁã¨ÍÂèÒãªéÀÒÉÒÇÔºÑµÔ ½Ö¡¾ÔÁ¾ìÊÑÅѡɳìÊÑ¡¹Ô´ ªÕÇÔµ(¤¹µÍºáÅФ¹¶ÒÁ)¨Ð§èÒ¢Öé¹àÂÍÐ (¨ÃÔ§æ¹Ð) Stay Hungry. Stay Foolish. |
#14
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¤×Í¢Íâ·É¤ÃѺàÁ×èÍ¡Õé¤Ô´ÁÒ¡ä»à˹×èÍÂ
4. a^4+a^2+2= (a^2+2)(a^2-1)Íѹ¹Õé¹èÒ¨Ðãªè¹Ð¤ÃѺ ÍÕ¡¢éͤ×Í x^6-125y^3=[x-5y][(x^2)^2+x^25y+5^2y^2] Êèǹ¢éÍ 10¹Õè àÍÍ x4+4y4=(x2−2xy+2y2)(x2+2xy+2y2) àÁ×èÍà»ç¹ÊٵõÒµÑÇ·Õè ¾Ê ¡ÅÒ§µéͧÁÕà¤Ã×èͧËÁÒµèÒ§¡Ñ¹ËÃ×Íà»ÅèÒ¤ÃѺ ¨Ò¡¹Õé¼Á¢Í⨷Âì¾ËعÒÁà¾ÔèÁÍÕ¡ä´éäËÁ¤ÃѺäÇé½Ö¡
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·Õè¤ÓµÍº¤Ø³äÁèàËÁ×͹¤¹Í×è¹à¾Õ§¤¹à´ÕÂÇ ÍÒ¨äÁèãªé¤Ø³¼Ô´ áµèÍÒ¨à¾ÃÒФ¹Í×è¹à¤éÒ¼Ô´¡çä´é |
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