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#1
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¢éÍÊͺ ÁËÔ´Å 2553
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à´Ç¼ÁÁÒâ¾Êµìà·èÒ·Õè¨Óä´é¹Ð æ 15 ¾ÄȨԡÒ¹ 2009 21:32 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 1 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ RT,,Ant~* |
#2
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1.¡Ó˹´àÅ¢ 1 , 3 , 6 , 10 , ... , n
ãËéàÅ¢¹Õéá·¹¨Ó¹Ç¹ÊÒÁàËÅÕèÂÁ·Õèà»ç¹ä»ä´é ¨§ËҨӹǹÊÒÁàËÅÕèÂÁ·ÕèÁÒ¡·ÕèÊØ´·Õè¹éÍ¡ÇèÒ 2009 2.â¹ÅÙ¡àµëÒ 4 ÅÙ¡ 1 ¤ÃÑé§ ¨§ËÒ¤ÇÒÁ¹èÒ¨Ðà»ç¹·Õè¨Ðä´é¼Å¤Ù³¢Í§áµéÁà·èҡѺ 36 3. ãËéNà»ç¹¨Ó¹Ç¹¹Ó⪤à»ç¹¨Ó¹Ç¹àµçÁµÃÑé§áµè1000-9999ÁÕËÅѡ˹èÇÂáÅÐËÅÑ¡¾Ñ¹¤×Í1 ¼ÅÃÇÁ¢Í§¨Ó¹Ç¹¹Ó⪤·Ø¡¨Ó¹Ç¹à·èҡѺà·èÒã´ $a^2 +b^2+c^2 +2a -4b +6c +14 \leqslant 0 $ ¨§ËÒ b-2ac _____________________________________ $ãËé x à»ç¹¨Ó¹Ç¹à©¾ÒÐ áÅÐ y à»ç¹¨Ó¹Ç¹àµçÁºÇ¡ ·ÕèÊÍ´¤Åéͧ¡Ñº 99x+1 = y^2 ¨§ËҼźǡ¢Í§¤èÒ y ·Õèà»ç¹ä»ä´é $ 1. 98 2. 99 3. 198 4. 199 Â×¹ÍÂÙ躹ËͤÍÂáËè§Ë¹Öè§ ÁͧàËç¹ÂÍ´àÊÒ¸§à»ç¹ÁØÁ¡éÁ (¢Í͹ØÒµÔãªé a) a áÅÐàËç¹°Ò¹àÊÒ¸§à»ç¹ÁØÁ B ãËé ËͤÍ¡ѺàÊÒ¸§ËèÒ§¡Ñ¹ y Á. (¼ÁÇèÒà¤éÒãËéËÒ¤ÇÒÁÊÙ§¢Í§Ëͤ͹éÐ) ¨§ËÒ¤ÇÒÁÊÙ§¢Í§ËͤÍ $ãËé ¤ÇÒÁÊÙ§¢Í§ ËͤÍ = h$ $ä´éÇèÒ \frac{sinA}{cosA} = \frac{h}{y}$ $ y(\frac{sinA}{cosA}) = h ---(1)$ áÅÐ $\frac{sinB}{cosB} = \frac{h}{y}$ $ y(\frac{sinB}{cosB}) = h ----(2)$ (1)=(2) $y(\frac{sinA}{cosA}) = y(\frac{sinB}{cosB}) $ . . . . . . . [/quote] ÍéÒ§ÍÔ§:
15 ¾ÄȨԡÒ¹ 2009 21:41 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 2 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ RT,,Ant~* |
#3
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ÊͺÁËÔ´Å ÁÕ⨷ÂìàÊÕ´éǹФÃѺ .
¹èҨзÕèÇèÒ æ ËÒÊèǹ·ÕèáÃà§Ò áµèäÁèÁÕÊèǹ·ÕèáÃà§Ò ?? |
#4
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ÍéÒ§ÍÔ§:
à¾ÔèÁ⨷Âì¤ÃѺ ⨷Âì¹èҨлÃÐÁÒ³æ¹Õé
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·ÓãËéàµçÁ·Õè·ÕèÊØ´ ÂѧÁÕ·ÕèÇèÒ§àËÅ×Íà¿×ͧ͢¤¹à¡è§·Õèà¼×èÍäÇéãË餹·Õè¾ÂÒÂÒÁ ÊÙéµèÍä»... ÁѹÂѧäÁ診á¤è¹Õ 14 ¾ÄȨԡÒ¹ 2009 17:07 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 1 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ ¤uÃÑ¡la¢ |
#5
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¢Í¤ÇÒÁ¡ÃسÒÁÒâ¾Êµì·ÕèÅÔ§¤ì´éÒ¹ÅéÒ§ ¨Ðä´éäÁ軹¡Ñ¹ ¤ÃѺ ¢Íº¤Ø³¤ÃѺ
http://www.mathcenter.net/forum/show...9059#post69059
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#6
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¢éÍ·Õè¡ÓÅѧ¨Ðâ¾Êµì¡çâ¾Êä» ËÁ´áÅéÇÅèФÃѺ 5+
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#7
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ÍèÍ ÁÕ¢é͹֧ à»ç¹¢éÍÊͺ ྪÃÂÍ´Á§¡Ø¯ 50 ´éǹéÐ
äÍ·Õè ÃÙ·ÂÒÇ æ æ ÍèÐËéÐ æ |
#8
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Mwit53
¢éÍ24) ãËéNà»ç¹¨Ó¹Ç¹¹Ó⪤à»ç¹¨Ó¹Ç¹àµçÁµÃÑé§áµè1000-9999ÁÕËÅѡ˹èÇÂáÅÐËÅÑ¡¾Ñ¹¤×Í1 ¼ÅÃÇÁ¢Í§¨Ó¹Ç¹¹Ó⪤·Ø¡¨Ó¹Ç¹à·èҡѺà·èÒã´ |
#9
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$a^2 +b^2+c^2 +2a -4b +6c +14 \leqslant 0 $
¨§ËÒ b-2ac _____________________________________ $ãËé x à»ç¹¨Ó¹Ç¹à©¾ÒÐ áÅÐ y à»ç¹¨Ó¹Ç¹àµçÁºÇ¡ ·ÕèÊÍ´¤Åéͧ¡Ñº 99x+1 = y^2 ¨§ËҼźǡ¢Í§¤èÒ y ·Õèà»ç¹ä»ä´é $ 1. 98 2. 99 3. 198 4. 199 ÊèǹµÑǼÁä´é 98 + 100 = 198 : ) 14 ¾ÄȨԡÒ¹ 2009 17:51 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 1 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ RT,,Ant~* |
#10
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¢éÍÊÒÁàËÅÕèÂÁÁØÁ©Ò¡µÍº AC = 185
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ÁÒËÒ¤ÇÒÁÃÙéäÇéµÔÇËÅÒ¹ áµèËÅÒ¹äÁèàÍÒàÅ¢áÅéÇ à¢éÒÁÒ·ÓàÅ¢àÍÒÁѹÍÂèÒ§à´ÕÂÇ ¤ÇÒÁÃÙéà»ç¹ÊÔè§à´ÕÂÇ·ÕèÂÔè§ãËé ÂÔè§ÁÕÁÒ¡ ÃÙéÍÐäÃäÁèÊÙé ÃÙé¨Ñ¡¾Í (¡àÇ鹤ÇÒÁÃÙé äÁèµéͧ¾Í¡çä´é ËÒäÇéÁÒ¡æáËÅдÕ) (áµè¡çÍÂèÒãËéÁÒ¡¨¹·èÇÁËÑÇ àÍÒµÑÇäÁèÃÍ´) |
#11
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ÍéÒ§ÍÔ§:
$99x = (y-1)(y+1)$ $x = 97 y = 98 $ $x = 101 y = 100 $ ____________________ 14 ¾ÄȨԡÒ¹ 2009 17:58 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 1 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ RT,,Ant~* |
#12
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ÍéÒ§ÍÔ§:
$99x+1 = y^2$ $y^2 - 1 = 99X$ $(y-1)(y+1) = (100-1)(100+1) -----> y = 100 $ $(y+1)(y-1) = (98+1)(98 - 1) -----> y = 98 $ ¼ÅºÇ¡¨Ö§à»ç¹ 100+98 = 198
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ÁÒËÒ¤ÇÒÁÃÙéäÇéµÔÇËÅÒ¹ áµèËÅÒ¹äÁèàÍÒàÅ¢áÅéÇ à¢éÒÁÒ·ÓàÅ¢àÍÒÁѹÍÂèÒ§à´ÕÂÇ ¤ÇÒÁÃÙéà»ç¹ÊÔè§à´ÕÂÇ·ÕèÂÔè§ãËé ÂÔè§ÁÕÁÒ¡ ÃÙéÍÐäÃäÁèÊÙé ÃÙé¨Ñ¡¾Í (¡àÇ鹤ÇÒÁÃÙé äÁèµéͧ¾Í¡çä´é ËÒäÇéÁÒ¡æáËÅдÕ) (áµè¡çÍÂèÒãËéÁÒ¡¨¹·èÇÁËÑÇ àÍÒµÑÇäÁèÃÍ´) |
#13
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ÍéÒ§ÍÔ§:
à¾ÃÒР⨷Âì¡Ó˹´ x à»ç¹¨Ó¹Ç¹à©¾ÒÐ àŵéͧ ä´é x = 97 ¡Ñº 101 ÍèФÃѺ áµèªéÍÂÊì¡çÊÇÂàÍÒ¡Òà æ ʹءÁÒ¡¤ÃѺ . ( áµèÇÔ·ÂìäÁè¤èÍÂàÍÒàÃ×èͧà·èÒäËÃè.. äÁèÁÑè¹ã¨ æ ) |
#14
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Â×¹ÍÂÙ躹ËͤÍÂáËè§Ë¹Öè§ ÁͧàËç¹ÂÍ´àÊÒ¸§à»ç¹ÁØÁ¡éÁ (¢Í͹ØÒµÔãªé a) a áÅÐàËç¹°Ò¹àÊÒ¸§à»ç¹ÁØÁ B
ãËé ËͤÍ¡ѺàÊÒ¸§ËèÒ§¡Ñ¹ y Á. (¼ÁÇèÒà¤éÒãËéËÒ¤ÇÒÁÊÙ§¢Í§Ëͤ͹éÐ) ¨§ËÒ¤ÇÒÁÊÙ§¢Í§ËͤÍ $ãËé ¤ÇÒÁÊÙ§¢Í§ ËͤÍ = h$ $ä´éÇèÒ \frac{sinA}{cosA} = \frac{h}{y}$ $ y(\frac{sinA}{cosA}) = h ---(1)$ áÅÐ $\frac{sinB}{cosB} = \frac{h}{y}$ $ y(\frac{sinB}{cosB}) = h ----(2)$ (1)=(2) $y(\frac{sinA}{cosA}) = y(\frac{sinB}{cosB}) $ ÂéÒ y ÁÒź áÅéÇ ¨Ñ´ÃÙ» ¡ç¨Ðä´é¤èҢͧ h ÍèФÃѺ * (¼Á¾ÔÁ¾ìäÁè¤èͨÐà¡è§à·èÒäËÃè æ ú¡Ç¹·ÓµèÍ´éǹФÃѺ) . . . . . . . 24 ¾ÄȨԡÒ¹ 2009 11:23 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 3 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ RT,,Ant~* |
#15
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·ÓãËéàµçÁ·Õè·ÕèÊØ´ ÂѧÁÕ·ÕèÇèÒ§àËÅ×Íà¿×ͧ͢¤¹à¡è§·Õèà¼×èÍäÇéãË餹·Õè¾ÂÒÂÒÁ ÊÙéµèÍä»... ÁѹÂѧäÁ診á¤è¹Õ 14 ¾ÄȨԡÒ¹ 2009 18:28 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 1 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ ¤uÃÑ¡la¢ |
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