Question

x+y+z=0 show that x cube +y cube +z cube = 3xyz
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Answer 1

Answer:

x³ + y³ +z³ =3xyz

Step-by-step explanation:

in the context of the given question ;

we have to find prove that x³ + y³ +z³ = 3xyz if x+y+z = 0

given ;

x+y+z = 0

we have to prove that;

x³ + y³ +z³ = 3xyz

we know that the identity if

x³ + y³ +z³ -3xyz =(x+y+z)(x²+y²+z²-xy-yz-zx)

but we already know that

(x+y+z=0)

so therefore;

x³ + y³ +z³ -3xyz =(0)(x²+y²+z²-xy-yz-zx)

x³ + y³ +z³ -3xyz =0

therefore,

x³ + y³ +z³ =3xyz

∴ Hence proved