Find all possible real triplet(s) (x,y,z) that satisfy the following system of equations:

     3 = √x + √y + √z,
     3 = x√x + y√y + z√z,
     3 = x2√x + y2√y + z2√z.

(3)+(1)-2*(2) =>

(x²-2x+1)√x+(y²-2y+1)√y+(z²-2z+1)√z=0

(x-1)²√x+(y-1)²√y+(z-1)²√z=0

=> (x-1)²√x=0 => x=1 or x=0

Similarly y=1 or y=0 and z=1 or z=0

But among these solutions only (1,1,1) satisfy all the given

conditions

Edited on October 13, 2008, 7:49 pm

Posted by Praneeth on 2008-10-13 19:42:44