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Grade 88 grade maths

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.

Profile image of Seema
10 Years agoGrade 8
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1 Answer

Profile image of Vikas TU
10 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.