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à¤Ã×èͧÁ×ͧ͢ËÑÇ¢éÍ | ¤é¹ËÒã¹ËÑÇ¢é͹Õé |
#1
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ÁÒªèÇ¡ҹ¤Ô´¤ÃѺ
1.ÁըӹǹàµçÁºÇ¡(a,b,c,d)·Ñé§ËÁ´¡ÕèªØ´ ·Õè 1/a+1/b+1/c+1/dà»ç¹¨Ó¹Ç¹àµçÁ
2.¨§ËÒ x+y+z â´Â·Õè (x\div y)\div z=8 (x\div y)-z=21 x-y=23 3.¡Ó˹´ãËé a áÅÐ b à»ç¹¤èÒ¤§·Õè«Ö觷ÓãËé ax+by=6 ax2+by2=12 <ax2=a¤Ù³¡Ñºx¡¡ÓÅѧÊͧ¹Ð¤ÃѺºº> ax3+by3=30 ax4+by4=84 ¨§ËÒax5+by5=à·èÒäËÃè (x\div y) ËÁÒ¤ÇÒÁÇèÒ x ËÒà y ¹Ð¤ÃѺ 04 ¾ÄÉÀÒ¤Á 2008 10:25 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 1 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ nongtum à˵ؼÅ: double post |
#2
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§§ ¤ÓÇèÒ \div ÍèФÃѺ ËÁÒ¤ÇÒÁÇèÒ $\frac{x}{y}$ ËÃ×ÍÇèÒ $\frac{y}{x}$ ¤ÃѺ
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#3
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⨷Âì¢éÍ 2. ¹èÒ¨Ðà»ç¹ÍÂèÒ§¹Õé¹Ð¤ÃѺ
2.¨§ËÒ x + y + z â´Â·Õè $(x\div y)\div z$ = 8 $(x\div y) - z$ = 21 x - y = 23 |
#4
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¢éÍ 2. x = 24 , y = 1, z = 3
·Ó¨Ò¡º¹Å§ÅèÒ§¤ÃѺ (x÷y)÷z = 8 --> ä´é (x÷y) = 8z áÅÐ x = 8zy (x÷y)−z = 21 --> á·¹ (x÷y) = 8z ¨Ðä´é 8z - z = 7z = 21 --> z = 3 á·¹ z = 3 ã¹ÊÁ¡ÒâéÒ§º¹ ¨Ðä´é x = 24y x - y = 23 --> á·¹ x = 24y ¨Ðä´é 24y - y = 23y = 23 ´Ñ§¹Ñé¹ y = 1, x = 24 |
#5
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ÍéÒ§ÍÔ§:
¨ÐàËç¹ÇèÒÂѧÁժش¢Í§ $\frac{1}{2}+\frac{1}{6}+\frac{1}{6} +\frac{1}{6}$ ËÃ×Í $\frac{1}{3}+\frac{1}{4}+\frac{1}{4} +\frac{1}{6}$ ËÃ×Í $\frac{1}{3}+\frac{1}{3}+\frac{1}{4} +\frac{1}{12} $à»ç¹µé¹ 09 ¾ÄÉÀÒ¤Á 2008 09:59 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 1 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ ËÂÔ¹ËÂÒ§ à˵ؼÅ: á¡é䢤ӵͺ |
#6
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ÍéÒ§ÍÔ§:
ÁÕ 1,1,1,1(1), 1,1,2,2(6), 2,2,2,2(1), 1,3,3,3(4), 4,4,4,4(1), 1,2,4,4(12), 1,2,3,6(24), 4,4,3,6(12), 3,3,6,6(6), 2,4,8,8(12), 2,4,6,12(24), 2,3,12,12(12), 3,3,4,12(12) á¤è13Ẻàͧ 05 ¾ÄÉÀÒ¤Á 2008 18:13 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 1 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ Puriwatt à˵ؼÅ: §§¤ÃѺ |
#7
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¨Ò¡à§×è͹ä¢â¨·Âì ¨Ðä´éÇèÒ ¤èҢͧ $\frac{1}{a}+\frac{1}{b}+\frac{1}{c} +\frac{1}{d} = 1, 2, 3$ ËÃ×Í $4$ à·èÒ¹Ñé¹
à¾×èÍãËéÊдǡ㹡ÒÃËҪش¢Í§¤ÓµÍº¡Ó¹Ë¹´ãËé $a\leqslant b\leqslant c\leqslant d$ Ẻ·Õè 1 ¶éÒ $\frac{1}{a}+\frac{1}{b}+\frac{1}{c} +\frac{1}{d} = 4$ ¨Ðä´é $(a,b,c,d)=(1,1,1,1)$ Ẻ·Õè 2 ¶éÒ $\frac{1}{a}+\frac{1}{b}+\frac{1}{c} +\frac{1}{d} = 3$ ¨Ðä´é $(a,b,c,d)=(1,1,2,2)$ Ẻ·Õè 3 ¶éÒ $\frac{1}{a}+\frac{1}{b}+\frac{1}{c} +\frac{1}{d} = 2$ ¨ÐàËç¹ÇèÒẺ·Õè 3 ¤èҢͧ a ·Õèà»é¹ä»ä´é ¤×Í 1 ¡Ñº 2 3.1 ¡Ã³Õ·Õè a = 1 ¨Ðä´é $(a,b,c,d)=(1,2,3,6)$, $(1,2,4,4), (1,3,3,3)$ 3.2 ¡Ã³Õ·Õè a = 2 ¨Ðä´é $(a,b,c,d)=(2,2,2,2)$ Ẻ·Õè 4 ¶éÒ $\frac{1}{a}+\frac{1}{b}+\frac{1}{c} +\frac{1}{d} = 1$ ¨ÐàËç¹ÇèÒẺ·Õè 4 ¤èҢͧ a ·Õèà»é¹ä»ä´é ¤×Í 2,3 ¡Ñº 4 4.1 ¡Ã³Õ·Õè a = 2 ¨Ðä´é $(a,b,c,d)=(2,3,7,42), (2,3,8,24), (2,3,9,18), (2,3,10,15), (2,3,12,12),$ $(2,4,5,20), (2,4,6,12), (2,4,8,8), (2,5,5,10), (2,6,6,6)$ 4.2 ¡Ã³Õ·Õè a = 3 ¨Ðä´é $(a,b,c,d)=(3,3,4,12), (3,3,6,6), (3,4,4,6)$ 4.3 ¡Ã³Õ·Õè a = 4 ¨Ðä´é $(a,b,c,d)=(4,4,4,4)$ µèͨҡ¹Ñ鹤§äÁèÂÒ¡áÅéǤÃѺ¡çà¾Õ§áµè´ÙÇèÒáµèÅÐẺ¨ÐÊÅѺ·Õè¡Ñ¹ä´é¡ÕèªØ´áÅéǹÓÁҺǡ¡Ñ¹¡çä´é¤ÓµÍºáÅéǤÃѺ 09 ¾ÄÉÀÒ¤Á 2008 09:57 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 1 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ ËÂÔ¹ËÂÒ§ à˵ؼÅ: ¾ÔÁ¾ì¢éͤÇÒÁà¡Ô¹ ÍÒ¨·ÓãËé¤Ó¹Ç³¼Ô´¾ÅÒ´ä´é |
#8
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¢Íº¤Ø³ÁÒ¡¤ÃѺ ¤Ø³ËÂÔ¹ËÂÒ§
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#9
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¢éÍ 3. ¼Áä´é¤ÓµÍº 246
áÅÐä´éáÊ´§ÇÔ¸Õ·Óã¹ Link ·ÕèṺÁÒ´éÇÂÍФÃѺ http://www.mathcenter.net/forum/show...57&postcount=5 06 ¾ÄÉÀÒ¤Á 2008 21:55 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 1 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ Puriwatt |
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