[MD-sorular] ***Denklem Sorusu***

[ihsan yÿfffffccel]

Soru : x + y + z = 1 

x^2 + y^2 + z^2 = 2 

x^3 + y^3 + z^3 = 3 ise

x^4 + y^4 + z^4 = ? 


Çözüm:



xy + yz + xz =1/2[(x + y + z)^2 – (x^2 + y^2 + z^2)] = -1/2

xyz = 1/3[x^3 + y^3 +z^3 –(x + y + z)(x^2 + y^2 + z^2)] = 1/6

x^4 + y^4 + z^4 = (x + y +z)( x^3 + y^3 +z^3) – (x^2 + y^2 + z^2)(xy + xz + yz) + xyz(x+ y +z) 

= 3 + 1 + 1/6 + 25/6 bulunur.

 

 

ihsan YÜCEL ---www.bilimadami.net---

(Matematik Moderatörü)

		
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