SOLUTION: If xy = a, xz = b, and yz = c, and none of these quantities is 0, then what is the x^2 - y^2 + z^2?

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Question 1064767: If xy = a, xz = b, and yz = c, and none of these quantities is 0, then what is the x^2 - y^2 + z^2?
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
If xy = a, xz = b, and yz = c, and none of these quantities is 0, then what is the x^2 - y^2 + z^2?

(1)  xy=a
(2)  xz=b
(3)  yz=c
(4)  x%5E2yz=ab   <--mult. equals by equals, (1) and (2)
(5)  xy%5E2z=ac   <--mult. equals by equals, (1) and (3)
(6)  xyz%5E2=bc   <--mult. equals by equals, (2) and (3)
(7)  x%5E2=%28ab%29%2F%28yz%29=%28ab%29%2Fc   <--div. both sides of (4) by yz
(8)  y%5E2=%28ac%29%2F%28xz%29=%28ac%29%2Fb   <--div. both sides of (5) by xz
(9)  z%5E2=%28bc%29%2F%28xy%29=%28bc%29%2Fa   <--div. both sides of (6) by xy
(10) x%5E2-y%5E2%2Bz%5E2=ab%2Fc-ac%2Fb%2Bbc%2Fa

Edwin