6

Part of 2003 Bosnia and Herzegovina Team Selection Test

Problems(1)

Bosnia and Herzegovina TST 2003 Day 2 Problem 3

Source: Bosnia and Herzegovina Team Selection Test 2003

a

b

c

be real numbers such that

\mid a \mid >2

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

. Prove that numbers

x

y

exist such that

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

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

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

algebrareal numbers