#1
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ÃÒ¡ÊÁ¡ÒõÃÕ⡳
ÍÂÒ¡·ÃÒºÇèÒàÃÒ¨ÐÊÃéÒ§ÊÁ¡Ò÷ÕèÁÕ cos(pi/9) , cos(2pi/9) ,cos(4pi/9)
à»ç¹ÃÒ¡¢Í§ÊÁ¡ÒÃä´éÍÂèÒ§ääÃѺ |
#2
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ÍéÒ§ÍÔ§:
µÑÇááÊÍ´¤Åéͧ cos 3A = 1/2, ÊͧµÑÇËÅѧÊÍ´¤Åéͧ cos 3A = -1/2 ¶éҵͺẺ·×èÍ æ ¡ç (x - cos(pi/9))(cos(2pi/9))(x-cos(4pi/9)) = 0 «Ö觶éÒ¡ÃШÒÂÍÍ¡ÁÒ¨ÐäÁèÊÇ ¶éÒ¨ÐãËéÊÇ µéͧàÅè¹ÊÁ¡ÒáÓÅѧˡàÅ cos 3A = 1/2 ¡Ñº cos 3A = -1/2 ÁÒÂÓÃÇÁ¡Ñ¹ ä´éÊÁ¡Òà $cos ^2 3A = 1/4$ «Ö觡ÃШÒÂáÅéǨÐä´éà»ç¹ $64x^6-96x^4+36x^2-1=0 , x = \cos A$ |
#3
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¢Íº¤Ø³ÁÒ¡¤ÃѺ
»Å. ¤×ͨÃÔ§æ¼Áµéͧ¡Ò÷ÃÒºÇèÒ¨ÐÊÃéÒ§ÊÁ¡Ò÷ÕèÁÕ cos(20),cos(40),cos(80) à»ç¹ÃÒ¡¢Í§ÊÁ¡Òà ä´éÍÂèÒ§ääÃѺ µéͧ¢Íâ·É¤Ø³ gon ´éǹФÃѺ ·Õè¼ÁÊ×èͤÇÒÁËÁÒ¼Դæä»ÍФÃѺ |
#4
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¤ÇÒÁ¨Ãԧ⨷Âì¢é͹ÕéÊǹФÃѺ ¤×Í ÊÁ¡ÒáÓÅѧÊÒÁ·ÕèÁÕÃÒ¡à»ç¹ cos20,cos40,cos80¹èÐÁÕ¤ÃѺáµèÍÂèÒ§·ÕèÇèÒÊÑÁ»ÃÐÊÔ·¸Ôì¨ÐäÁèŧµÑÇ
áµèÅͧÊѧࡵ´Õ´Õ¶éÒà»ÅÕ蹤èÒÃÒ¡à»ç¹ (-cos20),cos40,cos80¨Ð·ÓãËéä´éÊÁ¡ÒáÓÅѧÊÒÁ·ÕèÁÕÊÑÁ»ÃÐÊÔ·¸Ôìà»ç¹¨Ó¹Ç¹àµçÁ¾Í´ÕàŤ×Í $8x^{3}-6x+1=0$ |
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