SOLUTION: if x²+y²+z²-64/xy-yz-zx=-2 and x+y=3z,than value of z is?

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Question 896463: if x²+y²+z²-64/xy-yz-zx=-2 and x+y=3z,than value of z is?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%5E2%2By%5E2%2Bz%5E2-64%29%2F%28xy-yz-zx%29%22%22=%22%22-2

x%5E2%2By%5E2%2Bz%5E2-64%22%22=%22%22-2%28xy-yz-zx%29

x%5E2%2By%5E2%2Bz%5E2-64%22%22=%22%22-2xy%2B2yz%2B2zx

Since x%2By=3z, y=3z-x.  Substituting:

x%5E2%2B%283z-x%29%5E2%2Bz%5E2-64%22%22=%22%22-2x%283z-x%29%2B2%283z-x%29z%2B2zx

x%5E2%2B%289z%5E2-6xz%2Bx%5E2%29%2Bz%5E2-64%22%22=%22%22-6xz%2B2x%5E2%2B%286z-2x%29z%2B2zx

x%5E2%2B9z%5E2-6xz%2Bx%5E2%2Bz%5E2-64%22%22=%22%22-6xz%2B2x%5E2%2B6z%5E2-2zx%2B2zx

2x%5E2-6xz%2B10z%5E2-64%22%22=%22%222x%5E2-6xz%2B6z%5E2

10z%5E2-64%22%22=%22%226z%5E2

4z%5E2-64%22%22=%22%22%220%22

Divide through by 4

z%5E2-16%22%22=%22%22%220%22

Fctor

%28z-4%29%28z%2B4%29%22%22=%22%22%220%22

z-4 = 0;  z+4 = 0

  z = 4;    z = -4

Edwin