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Fantezi Cebir => Analiz-Cebir => Konuyu başlatan: stuart clark - Haziran 07, 2011, 09:05:46 ös

Başlık: denklem sistemi
Gönderen: stuart clark - Haziran 07, 2011, 09:05:46 ös

solve system of equations  (http://latex.codecogs.com/gif.latex?\left\{\begin{matrix}%20\displaystyle\frac{xy}{2x+3y}=5%20\\%20\displaystyle\frac{yz}{5y+2z}=3%20\\%20\displaystyle\frac{zx}{3z+5x}=2\\%20\end{matrix}\right.)

Where (http://latex.codecogs.com/gif.latex?x,y,z\in\mathbb{C})

Başlık: Ynt: denklem sistemi
Gönderen: Lokman Gökçe - Haziran 21, 2011, 04:36:30 ös

I hope that there is no a mistake my operations. I didn't check my solution.

Solution: clearly x, y,z are non-zero.

xy = 10x + 15y then, y = 10x/(x - 15) ... (1)

yz = 15y + 6z then, y = 6z/(z - 15) ... (2)

also we have zx = 30z + 50x ... (3)

from (1) and (2), we find 2zx = 75x - 45z ... (4)

by the equations (3), (4) we yields 21z = 5x ... (5)

let's solve (4) and (5) simultaneously. so, x = -180, z = 300/7. hence we find that y = 20/13.

Başlık: Ynt: denklem sistemi
Gönderen: stuart clark - Haziran 23, 2011, 06:08:04 öö

Thanks

Yes you are right scarface

Başlık: Ynt: denklem sistemi
Gönderen: cancan - Haziran 25, 2011, 06:28:27 ös

It must (x,y,z)=(180/11 , 120 , 300/19).