Roots of Two Polynomials
Source: 1977 USAMO Problem 3
April 4, 2010
algebrapolynomial
Problem Statement
If and are two of the roots of x^4\plus{}x^3\minus{}1\equal{}0, prove that is a root of x^6\plus{}x^4\plus{}x^3\minus{}x^2\minus{}1\equal{}0.