Freedom without limits is not freedom

Calculus Level 4

\[ \displaystyle \lim_{x \to \infty} \left ( \sqrt{x^4 + ax^3 + 3x^2 + bx + 2} - \sqrt{x^4 + 2x^3 - cx^2 + 3x - d} \ \right ) \]

The limit above equals to 4 for constants \(a,b,c,d\).

What is the value of the expression below?

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

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