#1
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àŢ¡¡ÓÅѧ SOS
¶éÒ a¡¡ÓÅѧx=b/c , b¡¡ÓÅѧy=c/a , c¡¡ÓÅѧz=a/b áÅéÇ xyz+x+y+z = ?
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#2
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SOS
¶éÒ a¡¡ÓÅѧx=b/c , b¡¡ÓÅѧy=c/a , c¡¡ÓÅѧz=a/b áÅéÇ xyz+x+y+z = ?
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#3
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ÍéÒ§ÍÔ§:
$b^y=\dfrac{c}{a}=\dfrac{c^{1+1/x}}{b^{1/x}}$ $b=c^{\frac{x+1}{xy+1}}$ $\therefore a=c^{\frac{1-y}{1+xy}}$ $c^z=\dfrac{c^{\frac{1-y}{1+xy}}}{c^{\frac{x+1}{xy+1}}}=c^{-\frac{x+y}{xy+1}}$ $z=-\dfrac{x+y}{xy+1}$ $\dfrac{x+y+z+xyz}{xy+1}=0$ $x+y+z+xyz=0$ |
#4
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¤Ø³á¿Ãì áÅФس nooonuii ¢Íº¤Ø³ÁÒ¡¤ÃѺ
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#5
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¨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 $xyz+x+y+z = 0$ |
#6
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¤Ø³ Puriwatt ¢Íºã¨¨ÃÔ§æ¹èÐ
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à¤Ã×èͧÁ×ͧ͢ËÑÇ¢éÍ | ¤é¹ËÒã¹ËÑÇ¢é͹Õé |
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