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xyz radicals (Posted on 2008-10-13) Difficulty: 3 of 5
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.

See The Solution Submitted by Bractals    
Rating: 4.0000 (1 votes)

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Solution Solution | Comment 3 of 4 |

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

(x-2x+1)√x+(y-2y+1)√y+(z-2z+1)√z=0

(x-1)√x+(y-1)√y+(z-1)√z=0

=> (x-1)√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

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