Let a and b be the roots of the equation x^2 - mx + 2 = 8x + 1/m. Suppose that a + 1/b and b + 1/a are the roots of the equation x^2-px+q=0. Compute p/q.
+128407 a + 1/b = (ba + 1) / b
b + 1/a = (ba + 1) / a
By Vieta
The sum of the roots = p = a(ba + 1) + b (ba + 1) (ab + 1) (a + b)
__________________ = ____________
ab ab
The product of the roots = q = (ab + 1)^2 / ab
(ab + 1) ( a + b) a + b
p/q = _______________ = ________
(ab + 1)^2 ab + 1
