Let a and b be the roots of \(7x^2-x-3=0\)
Find \( (1 + a + a^2 + a^3 + \dotsb)(1 + b + b^2 + b^3 + \dotsb)\)
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.
