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If x+y+z=0 find x^2 (y+z) +y^2 (z+x) + z^2 (x+y) Generally for such questions we use x=2, y=z=-1 thus making x+y+z=0 My query is, why can't we use x=-2, y=z=1, this also makes x+y+z=0? Both of these values are giving different answer in the above equation. Suggestions please. Thank you.

If x+y+z=0 find x^2 (y+z) +y^2 (z+x) + z^2 (x+y)
Generally for such questions we use x=2, y=z=-1 thus making x+y+z=0
My query is, why can't we use x=-2, y=z=1, this also makes x+y+z=0?
Both of these values are giving different answer in the above equation.
Suggestions please. 
Thank you. 

Grade:8

1 Answers

Vikas TU
14149 Points
6 years ago
From identity remember,

If x+y+z=0  then x^3 + y^3 + z^3 = 3xyz.
In given function of x,y,z
 x^2 (y+z) +y^2 (z+x) + z^2 (x+y) = it becomes = -( x^3 + y^3 + z^3) = -3xyz
 
which is the required answer.
 

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