MathDB

2013 HMMT Algebra #8: System of Rational Equations

Source:

February 17, 2013

HMMTcomplex numbers

Problem Statement

Let

x,y

be complex numbers such that

\dfrac{x^2+y^2}{x+y}=4

and

\dfrac{x^4+y^4}{x^3+y^3}=2

. Find all possible values of

\dfrac{x^6+y^6}{x^5+y^5}