If `|[x^3+1,x^2y,x^2z],[xy^2,y^3+1,y^2z],[xz^2,yz^2,z^3+1]|=15`, then the value of `(x^3+y^3+z^3)` equals

If x=3, y=2 and z=-1 , then the value of (x^3+y^3+1)/(y^3-z^3) is

If x, y, z are all distinct and |(x,x^(2),1+x^(3)),(y,y^(2),1+y^(3)),(z,z^(2),1+z^(3))|=0 then value of x y z is :

If x+y+z=12 and x^2+y^2+z^2=96 and 1/x+1/y+1/z=36 , then find the value of x^3+y^3+z^3

If x+y+z=0 then what is the value of (x^2)/(3z)+(y^3)/(3xz)+(z^2)/(3x) ?

If x,y,z in R and |{:(x,y^2,z^3),(x^4,y^5,z^6),(x^7,y^8,z^9):}|=2 then find the value of |{:(y^5z^6(z^3-y^3),x^4z^6(x^3-z^3),x^4y^5(y^3-x^3)),(y^2z^3(y^6-z^6),xz^3(z^6-x^6), xy^2(x^6-y^6)),(y^2z^3(z^3-y^3),xz^3(x^3-z^3),xy^2(y^3-x^3)):}|

If x = 2a- 1, y = (2a - 2) and z =3 - 4a, then the value of x ^(3) + y ^(3) + z ^(3) will be :

Prove that |[x,y,z] , [x^2, y^2, z^2] , [yz, zx, xy]| = |[1,1,1] , [x^2, y^2, z^2] , [x^3, y^3, z^3]|

If x:y=2:3 , y:z=3:4 , z:k=1:2 , find the value of x:y:z:k