Freedom without limits is not freedom

Calculus Level 4

limx(x4+ax3+3x2+bx+2x4+2x3cx2+3xd ) \displaystyle \lim_{x \to \infty} \left ( \sqrt{x^4 + ax^3 + 3x^2 + bx + 2} - \sqrt{x^4 + 2x^3 - cx^2 + 3x - d} \ \right )

The limit above equals to 4 for constants a,b,c,da,b,c,d.

What is the value of the expression below?

a+c+(b4d5)(a10c) a + c + \left ( b - \frac {4d}{5} \right ) \left ( a - \frac {10} c \right )

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