If `(x)/(a)=(y)/(b)=(z)/(c)`, then prove that each ratio is equal to `((3x^(3)-11y^(3)+13z^(3))/(3a^(3)-11b^(3)+13c^(3)))^((1)/(3))`

If (2x-3y)/(3z+y)=(z-y)/(z-x)=(x+3z)/(2y-3x) , then prove that every ratio is x/y

If x^a=y^b=z^c " and "y^3=zx , then prove that b(c+a)=3ca .

If x=(b-c)(a-d),y=(c-a)(b-d),z=(a-b)(c-d) , then the what is x^(3)+y^(3)+z^(3) equal to?

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

If x/(3x-y-z)=(y)/(3y-z-x)=(z)/(3z-x-y) and x+y+z=0 then show that the value of each of the ratio is equal to 1.

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

If x/(a)=y/(b)=z/(c) show that x^(3)/(a^(3))+y^(3)/(b^(3))+z^(3)/(c^(3))=(3xyz)/(abc)

If a, b, c, x, y and z be real numbers and x^(2)+y^(2)+z^(2)=16 , a^(2)+b^(2)+c^(2)=9 and ax+by+cz=12 ; the value of ((a^(3)+b^(3)+c^(3))^((1)/(3)))/((x^(3)+y^(3)+z^(3))^((1)/(3))) is