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-3<=(x^2+ax+b)/(x^2-x+1)<=2 (II Soros Olympiad 1995-96 R1 11.1)

Source:

June 3, 2024

algebrainequalities

Problem Statement

Find

a

and

b

for which the largest and smallest is values of the function

y=\frac{x^2+ax+b}{x^2-x+1}

are equal to the

2

and

-3

respectively.