If `x/a=y/b=z/c` show that each of these is equal to `((l x^(-3)+ m y^(-3)+nz^(-3))/(l a^(-3) + m b^(-3) +n C^(-3)))^(1/3)`

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

(a) If x + y + z=0, show that x ^(3) + y ^(3) + z ^(3)= 3 xyz. (b) Show that (a-b) ^(3) + (b-c) ^(3) + (c-a)^(3) =3 (a-b) (b-c) (c-a)

(a) If x + y + z=0, show that x ^(3) + y ^(3) + z ^(3)= 3 xyz. (b) Show that (a-b) ^(3) + (b-c) ^(3) + (c-a)^(3) =3 (a-b) (b-c) (c-a)