The value of

$$\frac{(1.121)^3 - (3.333)^3 + (2.212)^3}{(1.121)(3.333)(2.212)}$$ is

Expression : $$E=\frac{(1.121)^3 - (3.333)^3 + (2.212)^3}{(1.121)(3.333)(2.212)}$$

Let $$x=1.121,y=2.212,z=-3.333$$ and hence $$x+y+z=0$$ ------------(i)

=> $$E=-\frac{(x)^3+(y)^3+(-z)^3}{xy(-z)}$$ -----------(ii)

We know that, $$x^3+y^3+z^3-3xyz=(x+y+z)(x^2+y^2+z^2-xy-yz-zx)$$

=> $$x^3+y^3+z^3=3xyz$$ -------(iii)    [$$\because x+y+z=0$$]

Thus, substituting value from equation (iii) in equation (ii), we get : $$E=-3$$

=> Ans - (C)