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#1
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¼Á¼Ô´ËÃ×Íà©Å¼Դ¡Ñ¹á¹è
¤×ͼÁÇèÒÇÔ¸Õ¤Ô´¼Á¶Ù¡¹Ðáµèà©ÅÂÁѹ¹èҨмԴàÍÒà»ç¹ÇèÒÅͧ´Ù⨷ÂìÇÔ¸Õ¤Ô´¢Í§¼ÁáÅÐà©Å¡ѹ´Õ¡ÇèҤѺ
⨷Âì 1.$a^{4x}=3-2\sqrt{2}$ $a^{-4x}=\frac{1}{3-2\sqrt{2}} $ áÅéÇ $\frac{a^{6x}+a^{-6x}}{a^{2x}+a^{-2x}}$ ÁÕ¤èÒà»ç¹à·èÒã´ ÇԸբͧ¼Á $$3-2\sqrt{2}=(1-\sqrt{2})^2$$ $$´Ñ§¹Ñé¹ a^{2x}= 1-\sqrt{2}$$ $$áÅÐ a^{-4x}=(1+\sqrt{2})^2 $$ $$´Ñ§¹Ñé¹ a^{-2x}= 1+\sqrt{2}$$ $$\frac{(1+\sqrt{2})^3+(1-\sqrt{2})^3}{2}$$ $$\frac{(1+\sqrt{2})^3+(1-\sqrt{2})^3}{2}=7$$ ÇÔ¸Õà©Å $\frac{a^{6x}+a^{-6x}}{a^{2x}+a^{-2x}} =\frac{(a^{2x})^3+(a^{-2x})^3}{a^{2x}+a^{2x}}$ $$\frac{(a^{2x}+a^{-2x})(a^{4x}-a^{4x}a^{-4x}+a^{-4x})}{a^{2x}+a^{-2x}}$$ $$a^{4x}-1+a^{-4x}$$ $$3-2\sqrt{2}-1+3+2\sqrt{2}$$ $$=5$$
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»Õ˹éÒ¿éÒãËÁè ¨Ñ´¡Ñ¹ä´é·Õè¤èÒ¿ÔÊÔ¡Êì 31 ÁÕ¹Ò¤Á 2009 20:38 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 2 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ Platootod |
#2
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¼ÁÇèÒ·Õèà¢Òà©Å¶١áÅéǤÃѺ
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#3
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$(1-\sqrt{2})^2\ \not= 3-2\sqrt{2}$
¹Ð¤ÃѺ ´Ù´Õæ
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·ÓãËéàµçÁ·Õè·ÕèÊØ´ ÂѧÁÕ·ÕèÇèÒ§àËÅ×Íà¿×ͧ͢¤¹à¡è§·Õèà¼×èÍäÇéãË餹·Õè¾ÂÒÂÒÁ ÊÙéµèÍä»... ÁѹÂѧäÁ診á¤è¹Õ |
#4
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à©Å¶١áÅéÇ
¢éÍàʹÍá¹Ðà¾×èͪԧÃÒ§ÇÑŵèÍä» ''¤ÇÒÁ¼Ô´àÅç¡æ¹éÍÂæ ã¹ àÃ×èͧãËèæ ·ÓéãËé¼Ô´¾ÅÒ´ãËèËÅǧ'' àªè¹ ºÃÔÉÑ· µÔ´ ÇѹËÁ´ÍÒÂؼԴ 50 ªÔé¹ ¤¹ÍÒ¨·éͧàÊÕÂä»ÁÒà¡Ô¹50¤¹(¡Ô¹´éÇ¡ѹ) ·º·Ç¹¹Ô´æ ªÕÇÔµ¡éÒÇ˹éÒ
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#5
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$(x-y)^2=x^2-2xy+y^2$
$(1-\sqrt{2} )^2=1^2-2(1)(\sqrt{2})+(\sqrt{2})^2$ $(1^2-2(1)(\sqrt{2})+(\sqrt{2})^2)=3-2\sqrt{2}$äÁèà·èҵçä˹¤Ñº
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»Õ˹éÒ¿éÒãËÁè ¨Ñ´¡Ñ¹ä´é·Õè¤èÒ¿ÔÊÔ¡Êì |
#6
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¼Á·ÃÒºÇèÒà©Å¶١áµè·ÕèÃé͹ã¨ÁÒ¡¤×ͼÁ¼Ô´µÃ§ä˹¤Ñº
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#7
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â·É·Õ´Ù¼Ô´¨Ø´
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31 ÁÕ¹Ò¤Á 2009 21:28 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 5 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ ¤usÑ¡¤³Ôm à˵ؼÅ: LATEX |
#8
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ÍéÒ§ÍÔ§:
¢Í¶ÒÁÍÕ¡¤ÃÑé§äÁèà·èҵçä˹¤Ñº
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»Õ˹éÒ¿éÒãËÁè ¨Ñ´¡Ñ¹ä´é·Õè¤èÒ¿ÔÊÔ¡Êì 31 ÁÕ¹Ò¤Á 2009 21:21 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 1 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ Platootod |
#9
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$$a^{2x}=\pm (1-\sqrt{2})$$
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#10
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ÍéÒ§ÍÔ§:
ÍéÒ§ÍÔ§:
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#11
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àÅ¢ªÕé¡ÓÅѧÁѹà»ç¹àÅ¢¤Ùè¹Ð¤ÃѺ áµè¼Á¡çäÁèÁÑè¹ã¨ÍèÐ
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#12
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- - ¼Á¡çäÁèà¢éÒ㨢ͧ¤Ø³ Ne[s]zA ¹Ð¤ÃѺ
áµè¼ÁÇèҢͧ¼Á ¹èÒ¨Ðà»ç¹¨Ø´¼Ô´à¾ÃÒÐ àÅ¢ªÕé¡ÓÅѧà»ç¹Åº áµèµÍ¹á·¹¤èÒá·¹¼Ô´ä»¹Ô´
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#13
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$a^{-4x}=\frac{1}{3-2\sqrt{2}}=\frac{1}{3-2\sqrt{2}}\times\frac{3+2\sqrt{2}}{3+2\sqrt{2}}=3+2\sqrt{2}=(\sqrt{2}+1)^2$
¼ÁÅͧàÍÒÊÔ觹ÕéÁÒÁѹÍÒ¨¨ÐªèÇÂÍÐäÃä´é¹Ð¤ÃѺ(ÁÑé§) ÃÒ¡·Õè2¢Í§ $a+b+2\sqrt{ab}$ ¤×Í $\pm (\sqrt{a}+\sqrt{b})$ àÁ×èÍ $a,b>0$ ÃÒ¡·Õè2¢Í§ $a+b-2\sqrt{ab}$ ¤×Í $\pm (\sqrt{a}-\sqrt{b})$ àÁ×èÍ $a>b>0$ áÅÐ $a+b\geqslant 2\sqrt{ab}$ |
#14
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¨Ø´¼Ô´¡ç¤×Í $a^{2x} = \sqrt{2}-1$ äÁèãªè $1-\sqrt{2}$ ¤ÃѺ
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#15
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áµè
$(1-\sqrt{2})^2=(\sqrt{2}-1)^2$ ¹Ð¤Ñº ᵶ֧Áѹ¨Ðà·èҡѺ $(\sqrt{2}-1)$ ¤èÒ¡çäÁèà»ÅÕ蹹ФѺ µÍº¤Ø³ nes $\sqrt{(a-b)^2}= \left|a-b\right|$ $a^{4x}=3-2\sqrt{2}$ $a^{2x}=\sqrt{(1-2\sqrt{2})^2}$ =$\left|1-2\sqrt{2}\right|$ ÍéÒ§ÍÔ§¨Ò¡ my math àÅèÁä˹¡çäÁèÃÙé
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»Õ˹éÒ¿éÒãËÁè ¨Ñ´¡Ñ¹ä´é·Õè¤èÒ¿ÔÊÔ¡Êì 01 àÁÉÒ¹ 2009 20:47 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 4 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ Platootod |
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