# Is this 'Calculus' or 'Algebra'?

Calculus Level 5

$I=\int_0^{\infty} x^{5} e^{-x} dx = ( 2m^{4}+m^{3}+5m+9)!$

Let the product of the real roots (of $$m$$) of the equation above be $$P$$ .

Given that $$a+b+c=P$$, for $$(a,b,c)\in R^{+}$$. Find the $$\text{ Maximum}$$ value of:

$\dfrac{ (2a^{2}-b^{2}-c^{2})+(b+c)^2}{a+1} + \dfrac{ (2b^{2}-a^{2}-c^{2})+(c+a)^2}{b+1} + \dfrac{ (2c^{2}-b^{2}-a^{2})+(a+b)^2}{c+1}$

Details and Assumptions:

$$\bullet$$ Give your answer approximately up-to$$\text{ 3 decimal places}$$

$$\bullet$$ The roots of the equation are not necessarily distinct.

×