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=0My 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.
Seema , 8 Years ago
Grade 8
1 Answers
Vikas TU
Last Activity: 8 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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