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?
<pre><b>
(1)  {{{xy=a}}}
(2)  {{{xz=b}}}
(3)  {{{yz=c}}}
(4)  {{{x^2yz=ab}}}   <--mult. equals by equals, (1) and (2)
(5)  {{{xy^2z=ac}}}   <--mult. equals by equals, (1) and (3)
(6)  {{{xyz^2=bc}}}   <--mult. equals by equals, (2) and (3)
(7)  {{{x^2=(ab)/(yz)=(ab)/c}}}   <--div. both sides of (4) by yz
(8)  {{{y^2=(ac)/(xz)=(ac)/b}}}   <--div. both sides of (5) by xz
(9)  {{{z^2=(bc)/(xy)=(bc)/a}}}   <--div. both sides of (6) by xy
(10) {{{x^2-y^2+z^2=ab/c-ac/b+bc/a}}}

Edwin</pre></b>