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2014-12-23T06:00:14+05:30

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you have given two equations only and there are three variables.  Hence one cannot solve for x as a numerical value.  But x can be found in terms of y and z.

     x + y + z = 15          --- 4
     (x + z) y + z x = 72
       (15 - y) y + z x = 72
          x = ( y^2 - 15 y + 72 ) / z  =  15 - y - z            ---  3

       then  y and z satisfy :  y^2 + z^2 - 15 (y+z) + y z +72 = 0      - -- 2
          you can solve for y in terms of z.

Further,
        (x+y+z)^2 - 2 (xy+yz+zx) = 15^2 - 2 * 72
              x^2 + y^2 + z^2 = 81    ----- equation 5

               81 - x^2  - 15 (y + z) + y z + 72 = 0
                    x^2 =  153 - 15 ( y + z ) + y z      --- 1

    substitute the value of y in terms of z,  then x can be obtained in terms of z.

1 5 1