Question

if x+ y +z = 0 then verify that x³+ y³+ Z ³=3 x y z

Answer 1

Heya!

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

But, x + y + z = 0

Therefore,

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

⇒ x³ + y³ + z³ - 3xyz = 0

⇒ x^3 + y^3 + z^3 = 3xyz

Hope it helps!!!!

Answer 2

given,

x +y + z=0

now,

x3 +y3 +z3 =3xyz

x3 +y3 +z3 -3xyz =0

then,

x3 +y3+z3 -3xyz =(x +y +z)(x2+y2 +z2 -2 (xy +yz+zx))

= 0(x2 +y2+z2 -2(xy +yz+xz)

=0