#1
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àµÃÕÂÁÊͺ ÁËÔ´Å
1) $ABC$ à»ç¹ÃÙ»ÊÒÁàËÅÕèÂÁ ÁÕ $\widehat{B}$ à»ç¹ÁØÁ©Ò¡ ÅÒ¡ $\overline{BD} $ µÑ駩ҡ¡Ñº $ \overline{AC} $ ·Õè¨Ø´ $D$ ·ÓãËé $AD : AC = 3 : 7$
¶éÒÍѵÃÒÊèǹ $\dfrac{BC}{AB}: BD = 1 : a$ áÅéÇ $a^2$ ÁÕ¤èÒà·èÒã´ 23 ¡ØÁÀҾѹ¸ì 2011 19:13 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 2 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ lek2554 |
#2
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ãËé AB = x
ãËé BD = a n ä´é $\frac{BC}{AB} = n -----> BC = n (AB) = n x$ AC = $\sqrt{x^2 + n^2x^2}$ $(a n)^2 = x^2 -(\frac{3}{7} \sqrt{x^2 + n^2x^2})^2$ -------- (1) $(a n)^2 = n^2 x^2 -(\frac{4}{7} \sqrt{x^2 + n^2x^2})^2$ -------- (2) (1) = (2) ä´é $n^2 = \frac{4}{3}$ á·¹¤èÒã¹ (1) $a^2 = \frac{3x^2}{7}$ ä´é $AC^2 = \frac{7x^2}{3}$ ä´é $BD^2 = \frac{4x^2}{7}$ ä´é $BC^2 = \frac{4x^2}{3}$ ä´é $AB^2 = x^2$ |
#3
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ÍѵÃÒÊèǹ㹤ӶÒÁ ´éÒ¹«éÒÂäÁèÁÕ˹èÇÂáµè´éÒ¹¢ÇÒÁÕ˹èÇ á¤è¹Õé¡çÃÙéáÅéÇÇèÒ¾ÔÁ¾ì¼Ô´ = =
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#4
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2) ¡Ó˹´ãËé a à»ç¹¨Ó¹Ç¹¹Ñº·ÕèÁÕ¤èÒäÁèà¡Ô¹ 2000 ¶éÒ a ÊÍ´¤Åéͧ¡ÑºÊÁºÑµÔ·Ø¡¢é͵èÍ仹Õé
¡. àÁ×èÍ $\dfrac{a}{21}$ à»ç¹¨Ó¹Ç¹àÈÉÊèǹá·é áÅéǵÑÇÊèǹ¨ÐµéͧÁÕ¤èÒà·èҡѺ 3 àÊÁÍ ¢. $14a=b^2$ àÁ×èÍ b à»ç¹¨Ó¹Ç¹¹Ñº áÅéǼźǡ¢Í§ a ·Õèà»ç¹ä»ä´é·Ñé§ËÁ´ÁÕ¤èÒà·èҡѺà·èÒã´ $1.\,896\quad2.\,1190\quad3.\,1778\quad4.\,1792 $ ¤Ø³ Amankris µÍºäÇéáÅéǤÃѺ http://www.mathcenter.net/forum/show...=12744&page=10 ».Å. ¢éÍ ¡. ¶éÒ´ÙµÒÁ¹ÔÂÒÁ¢Í§àÈÉÊèǹá·é http://th.wikipedia.org/wiki/%E0%B9%...B8%A7%E0%B8%99 ¼ÁÇèÒ·Õè¶Ù¡¤ÇÃà»ç¹áºº¹Õé¤ÃѺ " àÁ×èÍ $\dfrac{21}{a}$ à»ç¹¨Ó¹Ç¹àÈÉÊèǹá·é áÅéǵÑÇàÈɨеéͧÁÕ¤èÒà·èҡѺ 3 àÊÁÍ" 23 ¡ØÁÀҾѹ¸ì 2011 22:10 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 5 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ lek2554 |
#5
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¤×ͶéÒÍѵÃÒÊèǹà»ç¹áºº¹Õé¨ÃÔ§ ¤èÒ a ÁѹµéͧÁÕäÁè¨Ó¡Ñ´ÍÂÙèáÅéǤÃѺ
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#6
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ź´Õ¡ÇèÒ ÍѹµÃÒÂ
22 ¡ØÁÀҾѹ¸ì 2011 20:57 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 1 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ Amankris |
#7
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µÍº 9 »Ð¤ÃѺ
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#8
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Êè§ÁÒ·Ò§ PM ËÃ×Í eyeshield21_Surf@windowslive.com ¡çä´é¤ÃѺ ^^
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#9
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#7
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#10
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3) ¡Ó˹´¾ËعÒÁ $x^4+a_1x^3+a_2x^2+a_3x+a_4$ ÊÍ´¤Åéͧ¡ÑºÊÁºÑµÔ·Ø¡¢é͵èÍ仹Õé
¡.$\quad a_1,a_2,a_3,a_4$ à»ç¹¨Ó¹Ç¹àµçÁ ¢.$\quad\sqrt{2} +\sqrt{3}$ à»ç¹¤ÓµÍº¢Í§ÊÁ¡Òà $x^4+a_1x^3+a_2x^2+a_3x+a_4=0$ ¨§ËÒ¤èҢͧ $a_1-a_2+a_3-2a_4$ 23 ¡ØÁÀҾѹ¸ì 2011 19:14 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 1 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ lek2554 |
#11
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ÍéÒ§ÍÔ§:
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#12
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4) ÃٻỴàËÅÕèÂÁ·ÕèÁÕ´éÒ¹ÂÒÇ 1, 2, 1, 2, 1, 2, 1, 2 ˹èÇ µÒÁÅӴѺ ṺÍÂÙèã¹Ç§¡ÅÁ ´Ñ§ÃÙ»
$\quad$¶éÒ $R$ à»ç¹ÃÑÈÁբͧǧ¡ÅÁǧ¹Õé áÅÐ $R^2=\dfrac{a+b\sqrt{2} }{2} $ áÅéÇ $2(a+b) $ ÁÕ¤èÒà·èÒã´ 23 ¡ØÁÀҾѹ¸ì 2011 23:11 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 2 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ lek2554 à˵ؼÅ: à¾ÔèÁÃÙ» |
#13
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#14
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#15
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ÍéÒ§ÍÔ§:
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