Mathcenter Forum  

Go Back   Mathcenter Forum > ¤³ÔµÈÒʵÃìÁѸÂÁÈÖ¡ÉÒ > »Ñ­ËÒ¤³ÔµÈÒʵÃì Á. µé¹
ÊÁѤÃÊÁÒªÔ¡ ¤ÙèÁ×Í¡ÒÃãªé ÃÒª×èÍÊÁÒªÔ¡ »¯Ô·Ô¹ ¤é¹ËÒ ¢éͤÇÒÁÇѹ¹Õé ·Óà¤Ã×èͧËÁÒÂÍèÒ¹·Ø¡ËéͧáÅéÇ

µÑé§ËÑÇ¢éÍãËÁè Reply
 
à¤Ã×èͧÁ×ͧ͢ËÑÇ¢éÍ ¤é¹ËÒã¹ËÑÇ¢é͹Õé
  #1  
Old 21 ÁԶعÒ¹ 2014, 18:58
kmaip1 kmaip1 äÁèÍÂÙèã¹Ãкº
ËÑ´à´Ô¹ÅÁ»ÃÒ³
 
Çѹ·ÕèÊÁѤÃÊÁÒªÔ¡: 05 àÁÉÒ¹ 2014
¢éͤÇÒÁ: 42
kmaip1 is on a distinguished road
Default àŢ¡¡ÓÅѧ SOS

¶éÒ a¡¡ÓÅѧx=b/c , b¡¡ÓÅѧy=c/a , c¡¡ÓÅѧz=a/b áÅéÇ xyz+x+y+z = ?
µÍº¾ÃéÍÁÍéÒ§ÍÔ§¢éͤÇÒÁ¹Õé
  #2  
Old 21 ÁԶعÒ¹ 2014, 19:00
kmaip1 kmaip1 äÁèÍÂÙèã¹Ãкº
ËÑ´à´Ô¹ÅÁ»ÃÒ³
 
Çѹ·ÕèÊÁѤÃÊÁÒªÔ¡: 05 àÁÉÒ¹ 2014
¢éͤÇÒÁ: 42
kmaip1 is on a distinguished road
Default SOS

¶éÒ a¡¡ÓÅѧx=b/c , b¡¡ÓÅѧy=c/a , c¡¡ÓÅѧz=a/b áÅéÇ xyz+x+y+z = ?
µÍº¾ÃéÍÁÍéÒ§ÍÔ§¢éͤÇÒÁ¹Õé
  #3  
Old 21 ÁԶعÒ¹ 2014, 22:01
nooonuii nooonuii äÁèÍÂÙèã¹Ãкº
¼Ùé¾Ô·Ñ¡Éì¡®·ÑèÇä»
 
Çѹ·ÕèÊÁѤÃÊÁÒªÔ¡: 25 ¾ÄÉÀÒ¤Á 2001
¢éͤÇÒÁ: 6,408
nooonuii is on a distinguished road
Default

ÍéÒ§ÍÔ§:
¢éͤÇÒÁà´ÔÁà¢Õ¹â´Â¤Ø³ kmaip1 View Post
¶éÒ $a^x=\dfrac{b}{c}, b^y=\dfrac{c}{a} , c^z=\dfrac{a}{b}$ áÅéÇ $xyz+x+y+z = ?$
$a=\dfrac{b^{1/x}}{c^{1/x}}$

$b^y=\dfrac{c}{a}=\dfrac{c^{1+1/x}}{b^{1/x}}$

$b=c^{\frac{x+1}{xy+1}}$

$\therefore a=c^{\frac{1-y}{1+xy}}$

$c^z=\dfrac{c^{\frac{1-y}{1+xy}}}{c^{\frac{x+1}{xy+1}}}=c^{-\frac{x+y}{xy+1}}$

$z=-\dfrac{x+y}{xy+1}$

$\dfrac{x+y+z+xyz}{xy+1}=0$

$x+y+z+xyz=0$
µÍº¾ÃéÍÁÍéÒ§ÍÔ§¢éͤÇÒÁ¹Õé
  #4  
Old 22 ÁԶعÒ¹ 2014, 13:11
kmaip1 kmaip1 äÁèÍÂÙèã¹Ãкº
ËÑ´à´Ô¹ÅÁ»ÃÒ³
 
Çѹ·ÕèÊÁѤÃÊÁÒªÔ¡: 05 àÁÉÒ¹ 2014
¢éͤÇÒÁ: 42
kmaip1 is on a distinguished road
Default

¤Ø³á¿Ãì áÅФس nooonuii ¢Íº¤Ø³ÁÒ¡¤ÃѺ
µÍº¾ÃéÍÁÍéÒ§ÍÔ§¢éͤÇÒÁ¹Õé
  #5  
Old 23 ÁԶعÒ¹ 2014, 16:23
Puriwatt's Avatar
Puriwatt Puriwatt äÁèÍÂÙèã¹Ãкº
ÅÁ»ÃÒ³äÃéÊÀÒ¾
 
Çѹ·ÕèÊÁѤÃÊÁÒªÔ¡: 14 ¡Ñ¹ÂÒ¹ 2006
¢éͤÇÒÁ: 1,435
Puriwatt is on a distinguished road
Default

¨Ò¡ $a^x= b/c, b^y= c/a, c^z= a/b$ ¨Ðä´éÇèÒ

$a^{xyz}= (a^x)^{yz}= (b/c)^{yz}= (b^{yz})/(c^{yz})=(c/a)^z(b/a)^y$

$a^{xyz}=(c^z×b^y)/a^{y+z}=(c/b)/a^{y+z} = a^{-(x+y+z)}$

¨Ñ´ÃÙ»ä´éà»ç¹ $a^{xyz+x+y+z}=1$ ´Ñ§¹Ñé¹ $xyz+x+y+z = 0$
µÍº¾ÃéÍÁÍéÒ§ÍÔ§¢éͤÇÒÁ¹Õé
  #6  
Old 24 ÁԶعÒ¹ 2014, 11:32
kmaip1 kmaip1 äÁèÍÂÙèã¹Ãкº
ËÑ´à´Ô¹ÅÁ»ÃÒ³
 
Çѹ·ÕèÊÁѤÃÊÁÒªÔ¡: 05 àÁÉÒ¹ 2014
¢éͤÇÒÁ: 42
kmaip1 is on a distinguished road
Default

¤Ø³ Puriwatt ¢Íºã¨¨ÃÔ§æ¹èÐ
µÍº¾ÃéÍÁÍéÒ§ÍÔ§¢éͤÇÒÁ¹Õé
µÑé§ËÑÇ¢éÍãËÁè Reply


à¤Ã×èͧÁ×ͧ͢ËÑÇ¢éÍ ¤é¹ËÒã¹ËÑÇ¢é͹Õé
¤é¹ËÒã¹ËÑÇ¢é͹Õé:

¤é¹ËÒ¢Ñé¹ÊÙ§

¡®¡ÒÃÊ觢éͤÇÒÁ
¤Ø³ äÁèÊÒÁÒö µÑé§ËÑÇ¢éÍãËÁèä´é
¤Ø³ äÁèÊÒÁÒö µÍºËÑÇ¢éÍä´é
¤Ø³ äÁèÊÒÁÒö Ṻä¿ÅìáÅÐàÍ¡ÊÒÃä´é
¤Ø³ äÁèÊÒÁÒö á¡é䢢éͤÇÒÁ¢Í§¤Ø³àͧä´é

vB code is On
Smilies are On
[IMG] code is On
HTML code is Off
·Ò§ÅÑ´ÊÙèËéͧ


àÇÅÒ·ÕèáÊ´§·Ñé§ËÁ´ à»ç¹àÇÅÒ·Õè»ÃÐà·Èä·Â (GMT +7) ¢³Ð¹Õéà»ç¹àÇÅÒ 22:00


Powered by vBulletin® Copyright ©2000 - 2024, Jelsoft Enterprises Ltd.
Modified by Jetsada Karnpracha