Ahaan's polynomial roots

Algebra Level 3

Suppose u u , v v , and w w are the roots of polynomial f(x)=x3+20x2+13x+42, f(x) = x^3 + 20x^2 + 13x + 42, and 1u \frac {1}{u} , 1v \frac {1}{v} , and 1w \frac {1}{w} are the roots of polynomial g(x)=x3+rx2+sx+t. g(x) = x^3 + rx^2 + sx + t. If g(1)=ab g(1) = \frac {a}{b} , where a a and b b are coprime positive integers, what is the value of a+b a + b?

This problem is posed by Ahaan Rungta.

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