1

Part of 1997 Vietnam National Olympiad

Problems(2)

Evaluate the maximum and minimum values

Source: Vietnam NMO 1997, Problem 1

Given a circle (O,R). A point P lies inside the circle, OP=d, d

geometryperimetergeometry proposed

Polynomial function

Source: Vietnam NMO 1997, Problem 4

Let k \equal{} \sqrt[3]{3}. a, Find all polynomials

p(x)

with rationl coefficients whose degree are as least as possible such that p(k \plus{} k^2) \equal{} 3 \plus{} k. b, Does there exist a polynomial

p(x)

with integer coefficients satisfying p(k \plus{} k^2) \equal{} 3 \plus{} k

algebrapolynomialfunctionalgorithmalgebra proposed