Maximum value for $M^4$ 
$$M=|\sqrt{x^2+4x+5}-\sqrt{x^2+2x+4}|$$
  Find the maximum value of $M^4$.

I think it could have a geometric solution. Because it looks like the difference between two points formula. Please help.

$$\sqrt{x^2+4x+5}=\sqrt{(x+2)^2+1^2}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(1)$$
$$\sqrt{x^2+2x+4}=\sqrt{(x+1)^2+(\sqrt{3})^2}~~~~~~~~~~~~~~~~~~~~~~~~(2)$$
$(1)$ is the distance of $(x,0)$ to $(-2,1)$ or $(-2,-1)$
$(2)$ is the distance of $(x,0)$ to $(-1,\sqrt{3})$ or $(-1,-\sqrt{3})$
