MathDB

Inequality from equality

Source:

March 18, 2014

inequalitiescalculusderivativequadraticsalgebra unsolvedalgebra

Problem Statement

For two real numbers a,b the equation:

x^{4}-ax^{3}+6x^{2}-bx+1=0

has four solutions (not necessarily distinct). Prove that

a^{2}+b^{2}\ge{32}