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.

Question

Vikas TU · Answer

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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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.

1 Answers

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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=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.

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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.