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Algebra Level 5

The sum of the real roots of f(x)=x43x34x23x+1=0f(x)=x^4-3x^3-4x^2-3x+1=0 can be represented as a+bc\large{\frac{a+\sqrt{b}}{c}}.

If a1+b1+c1=pqa^{-1}+b^{-1}+c^{-1}=\large{\frac{p}{q}} such that pp and qq are relatively prime positive integers, find the sum of the digits of (p+q)(p+q).

Details and Assumptions:

  • a1a^{-1} is the multiplicative inverse of aa.
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