[" If "x+y+z=0" show that "],[x^(2)+y^(2)+z^(2)=3xyz]

x+y+z=0 Show that x^(3)+y^(2)+z^(3)=3xyz

If x+y+z=0 show that x^(3)+y^(3)+z^(3)=3xyz .

If quad x+y+z=0 show that x^(3)+y^(3)+z^(3)=3xyz

If x+y+z=,0, show that x,y,zx^(2),y^(2),z^(2)y+z,z+x,x+y]|=0

If cos^(-1) x + cos^(-1) y + cos ^(-1) z = pi and 0 lt x,y,z lt 1 show that x^(2) +y^(2) +z^(2) +2xyz = 1

If cos^(-1)x + cos^(-1)y - cos^(-1) z = 0 , then show that x^(2) + y^(2) + z^(2) - 2xyz = 1

If x + y + z = 0 , show that x^3 + y^3 + z^3 = 3xyz .

If x+y+z=0, show that x^3 + y^3+z^3- 3xyz .