Verify: `(25xyz)((1)/(5)xyz)^(2)=x^(3)y^(3)z^(3)` for `x=2,y=1,z=2`

Prove the following : |{:(x,y,z),(x^(2),y^(2),z^(2)),(x^(3),y^(3),z^(3)):}|=|{:(x,x^(2),x^(3)),(y,y^(2),y^(3)),(z,z^(2),z^(3)):}|=xyz(x-y)(y-z)(z-x)

Show that |(x,y,z),(x^(2),y^(2),z^(2)),(x^(3),y^(3),z^(3))|=xyz (x-y) (y-z) (z-x)

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

If (2x-y)^(2)+(3y-z)^(2)=0 then x:y:z is

If x+y+z=0 and (x^(3)+y^(3))/(xyz)=(y^(3)+z^(3))/(xyz)=(x^(3)+z^(3))/(xyz)=a , then which of the following can be 'a'?

If x^(2)+9y^(2)+35z62=xyz((15)/(x)+(5)/(y)+(3)/(z)) then x,y,z in

Find the product of -5x^(2)y,-(2)/(3)xy^(2)z,(8)/(15)xyz^(2)and-(1)/(4)z .Verify the result when x=1,y=2 and z=3 .

verify that: x^(3)+y^(3)+z^(3)-3xyz=((1)/(2))(x+y+z)((x-y)^(2)+(y-z)^(2)+(z-x)^(2))

Prove that: {:|(x,y,z),(x^2,y^2,z^2),(x^3,y^3,z^3)|=|(x,x^2,x^3),(y,y^2,y^3),(z,z^2,z^3)| = xyz(x-y(y-z)(z-x)