MathDB

Bosnia and Herzegovina TST 2003 Day 2 Problem 3

Source: Bosnia and Herzegovina Team Selection Test 2003

September 18, 2018

algebrareal numbers

Problem Statement

Let

a

b

and

c

be real numbers such that

\mid a \mid >2

and

a^2+b^2+c^2=abc+4

. Prove that numbers

x

and

y

exist such that

a=x+\frac{1}{x}

b=y+\frac{1}{y}

and

c=xy+\frac{1}{xy}