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Let a and b be the roots of  \(7x^2-x-3=0\)

 

Find \( (1 + a + a^2 + a^3 + \dotsb)(1 + b + b^2 + b^3 + \dotsb)\)

 Feb 4, 2023
 #1
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By the quadratic formula, the roots of 7x^2 - x - 3 = 0 are (1 + sqrt(79))/14 and (1 - sqrt(79))/14.

 

Plugging them into the formula for an infinite geometric series, we get (1 + a + a^2 + a^3 + ...)(1 + b + b^2 + b^3 + ...) = 9/4.

 Feb 5, 2023

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