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 = x^{2}√x + y^{2}√y + z^{2}√z.
(3)+(1)2*(2) =>
(x²2x+1)√x+(y²2y+1)√y+(z²2z+1)√z=0
(x1)²√x+(y1)²√y+(z1)²√z=0
=> (x1)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 20081013 19:42:44 