MathDB

2014 preRMO p9, a,b roots of x^2-kx+l=0, a+1/b,b+1/a roots of x^2-px+q=0

Source:

August 9, 2019

algebratrinomialroots

Problem Statement

Natural numbers

k, l,p

and

q

are such that if

a

and

b

are roots of

x^2 - kx + l = 0

then

a +\frac1b

and

b + \frac1a

are the roots of

x^2 -px + q = 0

. What is the sum of all possible values of

q