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à¤Ã×èͧÁ×ͧ͢ËÑÇ¢éÍ | ¤é¹ËÒã¹ËÑÇ¢é͹Õé |
#1
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àµÃÕÂÁÊͺʾ°.2556
¾Õèæ¹éͧæ¤ÃѺ ªèÇ¡ѹPost⨷Âì·Õè¹èÒ¨Ðà»ç¹á¹Çʾ°.
â´Â·ÕèäÁèãªè¢éÍÊͺà¡èҹФÃѺ ¼ÁàÃÔèÁãËé¤ÃѺ 1.ËÒ¤èÒµèÓÊØ´¢Í§x^3+1/x^3 xà»ç¹¨Ó¹Ç¹ºÇ¡ 02 ÁÕ¹Ò¤Á 2013 21:47 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 1 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ ¿Ô¹Ô¡«ìàËÔ¹¿éÒ |
#2
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$\lim_{x \to -\infty}x^3+\frac{1}{x^3}= -\infty$
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#3
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2.
¡Ó˹´ãËé x à»ç¹ÊÁÒªÔ¡¢Í§¨Ó¹Ç¹¨ÃÔ§ºÇ¡ y à»ç¹ÊÁÒªÔ¡¢Í§¨Ó¹Ç¹¨ÃÔ§ ¨§ËÒÇèÒ $x^2+\frac{1}{x^2}+y^4+2y^2$ ÁÕ¤èÒµèÓÊØ´ËÃ×ÍäÁè ¶éÒÁÕ¨§áÊ´§ÇÔ¸ÕËÒ |
#4
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ÍéÒ§ÍÔ§:
$x^3+\frac{1}{x^3} \geqslant 2$ |
#5
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¢ÍÇÔ¸Õ·Ó´éǤÃѺ
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#6
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⨷Âì¹Õéà»ç¹â¨·Âì·Õè¼Áä´é¨Ò¡¤Ãٵ͹à»Ô´à·ÍÁ Á1 äÁèÃÙéÇèҨЧèÒÂÊÓËÃѺá¹Ç ʾ° ÃÖà»ÅèÒ
(2556-a)(2556-b)(2556-c)(2556-d)(2556-e)=2013 ¨§ËÒ¤èÒµèÓÊØ´¢Í§ a+b+c+d+e (ʾ° ¹ÕèÃͺááËÃ×ÍÃͺÊͧ¤ÃѺ) |
#7
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#8
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¤Çú͡´éÇÂÇèÒ a,b,c,d áÅÐ e à»ç¹ÊÁÒªÔ¡¢Í§¨Ó¹Ç¹ÍÐäÃ
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#9
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ÍéÒ§ÍÔ§:
$(2556-a)(2556-b)(2556-c)(2556-d)(2556-e)=2013 = 3 \times 11 \times 61 \times (-1) \times (-1)$ $(2556-a) = 3 \ \ \to \ a = 2553$ $(2556-b) = 11 \ \ \to \ b = 2545$ $(2556-c) = 61 \ \ \to \ c = 2495$ $(2556-d) = -1 \ \ \to \ d = 2557$ $(2556-e) = -1 \ \ \to \ e = 2557$ $a+b+c+d+e = 2,553+2,545+2,495+2,557+2,557 = 12,707$ EDIT ÁÒ¤Ô´´ÙÍÕ¡·Õ ¹èÒ¨ÐÁÕà§×èÍ¹ä¢ $ a, \ b, \ c, \ d, \ e \ $ à»ç¹¨Ó¹Ç¹àµçÁáÅÐÁÕ¤èÒµèÒ§¡Ñ¹ $(2556-a)(2556-b)(2556-c)(2556-d)(2556-e)=2013 = (-3) \times 11 \times 61 \times (1) \times (-1)$ $(2556-a) = -3 \ \ \to \ a = 2559$ $(2556-b) = 11 \ \ \to \ b = 2545$ $(2556-c) = 61 \ \ \to \ c = 2495$ $(2556-d) = 1 \ \ \to \ d = 2555$ $(2556-e) = -1 \ \ \to \ e = 2557$ $a+b+c+d+e = 2,559+2,545+2,495+2,555+2,557 = 12,711$
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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´) 05 ÁÕ¹Ò¤Á 2013 22:43 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 2 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ banker |
#10
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ÍéÒ§ÍÔ§:
¨Ð·ÓãËéä´é $a+b+c+d+e$ ÁÒ¡¢Öé¹ ä´éÁÑéÂÍèФÃѺ ÍÂÒ¡ÃÙéÍÕ¡ÍÂèÒ§ÍèФÃѺ àÇÅÒàÃÒ·ÓáÅéÇàÃÒ¨ÐËҪش¢Í§ 5 ¨Ó¹Ç¹áºº¹ÕéÂѧ䧷Õè¨ÐãËéä´éÁÒ¡·ÕèÊØ´¨ÃÔ§æÍèФÃѺ ẺÇèÒàÃÒÊÒÁÒöáÊ´§ä´éÇèÒÁѹÁÒ¡·ÕèÊØ´áÅéǨÃÔ§æ
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...ÊÕªÁ¾Ù¨ÐäÁè¨Ò§´éÇÂà˧×èÍ áµè¨Ð¨Ò§´éǹíéÒÅÒÂ... 03 ÁÕ¹Ò¤Á 2013 12:31 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 3 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ ~ArT_Ty~ |
#11
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ÍéÒ§ÍÔ§:
$(x+\frac{1}{x})^2 ¨ÐµèÓÊØ´à»ç¹ 2^2=4 ¨Ò¡ AM-GM$ $(y^2+1)^2 ¨ÐµèÓÊØ´à»ç¹ 1$ $(x+\frac{1}{x})^2+(y^2+1)^2-3 ¨ÐµèÓÊØ´à»ç¹ 4+1-3=2$
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¢Í»Åͺ㨵ÑÇàͧ˹è͹ФÃѺ: àÍÒ¹èÒ..¹Õèá¤èʹÒÁà´ÕÂÇ,¶×ÍÇèÒ¿Ò´à¤ÃÒÐËìÅСѹ ʹÒÁ˹éÒµéͧ´Õá¹è[à¤ÃÒÐËìâ´¹¿Ò´ä»à¡ÅÕé§áÅéǹÕè¹Ò] ÊÙéæ |
#12
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ÍéÒ§ÍÔ§:
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¢Í»Åͺ㨵ÑÇàͧ˹è͹ФÃѺ: àÍÒ¹èÒ..¹Õèá¤èʹÒÁà´ÕÂÇ,¶×ÍÇèÒ¿Ò´à¤ÃÒÐËìÅСѹ ʹÒÁ˹éÒµéͧ´Õá¹è[à¤ÃÒÐËìâ´¹¿Ò´ä»à¡ÅÕé§áÅéǹÕè¹Ò] ÊÙéæ |
#13
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AM GM ¤×ÍÍÐääÃѺ
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#14
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¤ÇÒÁÊÑÁ¾Ñ¹¸ì¢Í§¤èÒà©ÅÕè¹àÅ¢¤³Ôµ¡ÑºàâҤ³Ôµ¤ÃѺ
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#15
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...ÊÕªÁ¾Ù¨ÐäÁè¨Ò§´éÇÂà˧×èÍ áµè¨Ð¨Ò§´éǹíéÒÅÒÂ... |
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