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Problem Of The Week #476 July 20th 2021

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anemone

MHB POTW Director
Staff member
Feb 14, 2012
3,917
Here is this week's POTW:

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Let $a,\,b,\,c$ and $d$ be the roots to the polynomial $f(x)=x^4-3x^3+2x^2+5x-4$ . Evaluate $\left(a+1+\dfrac{1}{a}\right)\left(b+1+\dfrac{1}{b}\right)\left(c+1+\dfrac{1}{c}\right)\left(d+1+\dfrac{1}{d}\right)$.
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