If `x:a=y:b=z:c`, then `x^3/a^2+y^3/b^2+z^3/c^2=?`

If (x)/(a)=(y)/(b)=(z)/(c), then show that (x^(3)+a^(3))/(x^(2)+a^(2))+(y^(3)+b^(3))/(y^(2)+b^(2))+(z^(3)+c^(3))/(z^(2)+c^(2))=((x+y+z)^(3)+(a+b+c)^(2))/((x+b+z)^(2)+(a+b+c)^(2))

If x!=y!=za n d|[x,x^2, 1+x^3],[y ,y^2 ,1+y^3],[z, z^2, 1+z^3]|=0, then the value of x y z is a.1 b. 2 c. -1 d. 2

If x=a+m , y=b+m , z=c+m , the value of (x^2+y^2+z^2-y z-z x-x y)/(a^2+b^2+c^2-a b-b c-c a) is (a) 1 (b) (x+y+z)/(a+b+c) (c) (a+b+c)/(x+y+z) (d) not possible to find

If b+c = 2x, c+a =2y and a +b =2z then value of a^(3) +b^(3) +c^(3) is

If a=x-y,b=y-z and c=z-x then the value of a^(3)+b^(3)+c^(3)