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#1
30 ÁÕ¹Ò¤Á 2001, 16:12
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µÃÕ⡳ÁÔµÔ
¡Ó˹´ãËé XÍÂÙè㹪èǧ [0,45]ͧÈÒ ¨§ËҤӵͺ¢Í§ÊÁ¡ÒÃ
(sin2X)^2+(sin3X)^2+(sin4X)^2+(sin9X)^2=2 ÍÕ¡¢éͤѺ sec[arctan(XX-6x-1)^1/2]=cosec[arccot(X^1/2)]-1 
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#2
30 ÁÕ¹Ò¤Á 2001, 16:12
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¢éÍ 1.
à¹×èͧ¨Ò¡ cos2A=1-2(sinA)^2 (sinA)^2=(1-cos2A)/2 ´Ñ§¹Ñé¹ 1-cos4X+1-cos6X+1-cos8X+1-cos18X=4 (cos4X+cos18X)+(cos6X+cos8X)=0 2cos11Xcos7X+2cos7XcosX=0 cos7X(cos11X+cosX)=0 ¡Ã³Õáá cos7X=0 cos7X=cos(Pi/2) ¨Ðä´éÇèÒ 7X=2nPi+Pi/2 , 7X=2nPi-Pi/2 X=2nPi/7+Pi/14 , X=2nPi-Pi/14 ¤èÒ X ·ÕèÊÍ´¤Åéͧ¤×Í Pi/14 ¡Ã³Õ·ÕèÊͧ cos11X+cosX=0 cosX=cos(Pi+11X) ËÃ×Í cosX=cos(Pi-11X) Pi+11X=2nPi+X , Pi+11X=2nPi-X ËÃ×Í Pi-11X=2nPi+X , Pi-11X=2nPi-X X=(2n-1)Pi/10 , X=(2n-1)Pi/12 ËÃ×Í X=-(2n-1)Pi/12 , X=-(2n-1)Pi/10 ¤èÒ X ·ÕèÊÍ´¤Åéͧ¤×Í Pi/4,Pi/10,Pi/12 à¾ÃÒЩйÑ鹤ӵͺ¤×Í Pi/4,Pi/10,Pi/12,Pi/14 ¢éÍ 2. ãËé A=arctan(X^2-6X-1)^1/2 , B=arccot(X)^1/2 ´Ñ§¹Ñé¹ (tanA)^2=X^2-6X-1 , (cotB)^2=X à¹×èͧ¨Ò¡ (secA)^2-(tanA)^2=1 , (cosecB)^2-(cotB)^2=1 ¨Ðä´éÇèÒ (secA)^2=X^2-6X .....(1) , (cosecB)^2=X+1 .....(2) ¨Ò¡â¨·Âì secA=cosecB-1 (secA)^2=(cosecB)^2-2cosecB+1 X^2-6X=X+2-2cosecB X^2-7X-2=-2cosecB X^4+49X^2+4-14X^3-4X^2+28X=4X+4 X^4-14X^3+45X^2+24X=0 X(X^3-14X^2+45X+24)=0 X(X-8)(X^2-6X-3)=0 ´Ñ§¹Ñé¹ X=0,8,3+2root3,3-2root3 ¨Ò¡¡ÒõÃǨ¤ÓµÍº¾ºÇèÒãªéä´éà¾Õ§ 2 ¤èÒ¤×Í 8,3+2root3
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#3
30 ÁÕ¹Ò¤Á 2001, 16:13
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àÍ..¢éÍ 2 ¹èÐ á·¹¤èÒ´éÇ 8 ã¹â¨·Âì¨Ðä´éÇèÒ
4 = 3 - 1 äÁèãªèàËÃÍ Êèǹ 3+2sqrt3 ¡çäÁèà·èҡѹ(¢Õéà¡Õ¨¾ÔÁ¾ì)
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#4
30 ÁÕ¹Ò¤Á 2001, 16:14
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á·¹¤èÒ´éÇ 8 ¡é͡óշÕèà»ç¹Åºä§¤ÃѺ
¨Ðä´éÇèÒ -4= -3-1 Êèǹ 3+2root3 ¨Ðä´éÇèÒ root3=root3+1-1
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#5
30 ÁÕ¹Ò¤Á 2001, 16:15
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á·¹¤èÒ¶Ù¡áÅéǤÃѺ.
áµèäÁè¨Óà»ç¹µé᷹ͧ¤èÒ ¾Ô¨ÒóÒà§×è͹䢨ҡÃÙé· (x) ¡Ñº ÃÙé·(x^2 -x -6) ¡ç¾Í
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