Rational Function

Algebra Level 4

Consider the function f(x)=x2+ax+bx2+2x+3f(x)=\dfrac{x^{2}+ax+b}{x^{2}+2x+3} where aa and bb are positive integers.

If the range of f(x)f(x) is [5,4],[-5,4], find the value of a2+b2ab.a^{2}+b^{2}-ab.

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