Question

X+y+z=0 then what is x^2 by yz + y^2 by zx +z^2 by xy

Answer 1

Answer:

x^2 / yz + y^2 / zx + z^2 / xy = ( x^3 + y^3 + z^3 )/ xyz

now, if x + y+ z = 0 then x^3 + y^3 + z^3 = 3 xyz ( see at the end for better understanding )

now , x^3 + y^3 + z^3 / xyz = 3 xyz / xyz = 3

Step-by-step explanation:

x^3 + y^3 + z^3 - 3xyz = ( x + y + z ) ( x^2 + y^2 + z^2 - xy - yz - zx )

now if x + y + z = 0

x^3 + y^3 + z^3 - 3xyz = 0

x^3 + y^3 + z^3 = 3xyz