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The fourth degree polynomial equation x^4 - 7x^3 + 4x^2 + 7x - 4 = 0 has four real roots, a, b, c, and d. What is the value of the sum 1/(abc) + 1/(abd) + 1/(acd) + 1/(bcd)?

 Jun 24, 2021
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Note that $1/(abc) + 1/(abd) + 1/(acd) + 1/(bcd) = (a+b+c+d)/(abcd)$.  The values of $a+b+c+d$ and $abcd$ can be read off from the coefficients of $x^4-7x^3+4x^2+7x-4=0$ by Vieta's formula.
 

 Jun 24, 2021

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