Expert: Richard J. Raridon - 2/18/2004

Question
solve this system of equations

x^2 + y^2 + z^2 = 19^2

1/x + 1/y + 1/z = 0

x - y + z = 11

been trying to solve just going round in circles
need to know what methods to use please help think i've tried eveerything

Answer
The only way I know how to do it is trial and error.  
x,y, and z are all integers.  So x^2, for example, has to be 4,9,16,25, etc.  Therefore, y^2+z^2 has to be (361-4),
(361-9), (361-16), etc.  It didn't take too long to find the values are 6, 10, and 15.  One has to be negative to satisfy the second equation.  So one value is -6.  Look at the third equation and you can find x=15, y=-6, and z=10.