1

Part of 2002 Bosnia Herzegovina Team Selection Test

Problems(2)

Find 'a' for which max(x)-min(x)=8

Source: P1: Bosnia and Herzegovina TST 2002

x,y,z

be real numbers that satisfy

x+y+z= 3 \ \ \text{ and } \ \ xy+yz+zx= a

a

is a real parameter. Find the value of

a

for which the difference between the maximum and minimum possible values of

x

8

algebra proposedalgebra

Inequality with a^2+b^2+c^2=1; P4 : B&H TST 2002

Source:

a,b,c

be real numbers such that

a^2+b^2+c^2=1

\frac{a^2}{1+2bc}+\frac{b^2}{1+2ca}+\frac{c^2}{1+2ab} \ge \frac35