#16
|
|||
|
|||
2^2^2^2^2^.... ·Ñé§ËÁ´ 1001 µÑÇ
áÅÐ 3^3^3^3^.... ·Ñé§ËÁ´ 1000 µÑÇ áÅÐ 4^4^4^4^..... ·Ñé§ËÁ´ 999 µÑÇ µÑÇä˹ÁÕ¤èÒÁÒ¡·ÕèÊØ´ ªèÇÂ˹èͤÃѺ äÁèàËç¹·Ò§ÊÇèÒ§àÅ |
#17
|
|||
|
|||
ÍéÒ§ÍÔ§:
$x^2-\frac{1}{x^2} = (x-\frac{1}{x})(x+\frac{1}{x})$ $x^3-\frac{1}{x^3} = (x-\frac{1}{x})(.....) $ $x^4-\frac{1}{x^4}= (x-\frac{1}{x})(x+\frac{1}{x})(....)$ Ë.Ã.Á. $= x-\frac{1}{x} =3$ ....(1) $ x^2+\frac{1}{x^2} = 11$ ...(2) (1)x(2) $ \ \ \ x^3-\frac{1}{x^3} -(x-\frac{1}{x}) = 33$ $ x^3-\frac{1}{x^3} -(3) = 33$ $ x^3-\frac{1}{x^3} = 36$
__________________
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´) |
#18
|
|||
|
|||
ÍéÒ§ÍÔ§:
ÅͧẺµÑÇàÅ¢¹éÍÂæ 2^2^2^2 ... 4 µÑÇ ä´é $2^{16}$65536 3^3^3 ......3 µÑÇ ä´é $3^{27} \ $ÃÒÇæàÅ¢ 13 ËÅÑ¡ 4^4 ....2 µÑÇ ä´é $4^4 = 256$ 2^2^2^2^2 ... 5 µÑÇ ä´é àÅ¢ 2ËÁ×è¹ËÅÑ¡ 3^3^3^3 ......4 µÑÇ ä´é $3^{3^{27}} \ $ÃÒÇæàÅ¢ ÊÒÁÅéÒ¹ÅéÒ¹ ËÅÑ¡ 4^4^4....3 µÑÇ ä´é $4^{256} $ ä´éàÅ¢ÃÒÇæ 155 ËÅÑ¡ ¨Ö§ÊÃØ»ÇèÒ 3^3^3^3^.... ·Ñé§ËÁ´ 1000 µÑÇ ÁÒ¡·ÕèÊØ´ ÁÑèÇæẺ¹ÕéáËÅФÃѺ äÁèÃÙé¶Ù¡ËÃ×Íà»ÅèÒ ä»¹Í¹¡è͹¤ÃѺ ¾ÃØ觹Õé¤èÍÂÇèҡѹÍÕ¡·Õ
__________________
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´) |
#19
|
|||
|
|||
ÍéÍ ¢Íº¤Ø³¤ÃѺ µÍº $1-a^2$ ÃÖà»ÅèÒ¤ÃѺ?
|
#20
|
|||
|
|||
ÍéÒ§ÍÔ§:
¢Íº¤Ø³¤ÃѺ $2^{2x+2}-6^x-2(3^{2x+2})=0$ x ÁÕ¤èÒà·èÒã´ $(\frac{1}{2} )^{4x} = 3-2\sqrt{2} áÅéÇ \frac{2^{6x}-2^{-6x}}{2^{2x}-2^{-2x}}$ ÁÕ¤èÒà·èÒã´ 06 ¡Ã¡®Ò¤Á 2011 22:08 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 1 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ [T]ime[Z]ero |
#21
|
|||
|
|||
$2^{2x+2}-6^x-2(3^{2x+2})=0$
$ 4 \cdot 2^{2x}-2^x \cdot 3^x-2( 9 \cdot 3^{2x})=0$ $ 4 \cdot 2^{2x}-2^x \cdot 3^x- 18 \cdot 3^{2x})=0$ $(4 \cdot 2^x -9 \cdot 3^x)(2^x+2 \cdot 3^x) = 0 \ \ \ \ \ $ (¨ÐÁͧ $2^x =a, \ \ 3^x = b) \ $ ¡çä´é $( 2^{x+2} - 3^{x+2})(2^x+2 \cdot 3^x) = 0 \ \ \ \ \ $ ⨷ÂìäÁèä´é¡Ó˹´ÇèÒ $x$ à»ç¹¨Ó¹Ç¹»ÃÐàÀ·ã´ ã¹ÃдѺ Á. µé¹ ãËé $x$ à»ç¹¨Ó¹Ç¹àµçÁ¡çáÅéǡѹ $( 2^{x+2} - 3^{x+2}) = 0$ $ 2^{x+2} = 3^{x+2}$ $x = -2$ á·¹¤èÒáÅéÇ ÊÁ¡ÒÃà»ç¹¨ÃÔ§
__________________
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´) |
#22
|
|||
|
|||
ÍéÒ§ÍÔ§:
$2^{-4x} (2^{8x}+ 2^{4x} +1)$ $2^{4x} +1 + 2^{-4x}$ á·¹¤èÒ $(\frac{1}{2} )^{4x} = 2^{-4x} = 3-2\sqrt{2} $ $2^{4x} +1 + 2^{-4x} = \dfrac{1}{3-2\sqrt{2} } + 1 + (3-2\sqrt{2}) = \dfrac{3+2\sqrt{2}}{9-8} +1+ 3-2\sqrt{2} = 7$
__________________
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´) |
#23
|
||||
|
||||
Ẻ¹Õé§èÒ¡ÇèÒÁÑé¤ÃѺ ¤Ù³´éÇ $2^{2x}$ ·Ñé§àÈÉáÅÐÊèǹ
$$\frac{2^{6x}-2^{-6x}}{2^{2x}-2^{-2x}}=\frac{2^{8x}-2^{-4x}}{2^{4x}-1}$$ $$=\frac{(2^{4x})^2-2^{-4x}}{2^{4x}-1}$$ $$=\frac{(3+2\sqrt{2})^2-(3-2\sqrt{2})}{(3+2\sqrt{2})-1}$$ $$=\frac{14(1+\sqrt{2})}{2(1+\sqrt{2})}$$ $$=7$$
__________________
¤³ÔµÈÒʵÃì ¤×Í ÀÒÉÒÊÒ¡Å ¤³ÔµÈÒʵÃì ¤×Í ¤ÇÒÁÊǧÒÁ ¤³ÔµÈÒʵÃì ¤×Í ¤ÇÒÁ¨ÃÔ§ µÔ´µÒÁªÁ¤ÅÔ»ÇÕ´ÕâÍä´é·Õèhttp://www.youtube.com/user/poperKM |
#24
|
|||
|
|||
ÍéÒ§ÍÔ§:
¼ÁÃØè¹âºÏ ªÍºáºº¶Ö¡æ ÅÙ¡·Ø觪ͺÅØÂ
__________________
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´) |
#25
|
|||
|
|||
¢Íº¤Ø³¤ÃѺ
|
|
|