IMO 1989 LL ISR58

Let P1(x), P2(x), . . . , Pn(x) be polynomials with real coefficients.

imolonglistmathematicsolympiad

IMO 1989 LL ISR58

Origin: ISR

Problem

Let P1(x), P2(x), . . . , Pn(x) be polynomials with real coefficients. Show that there exist real polynomials Ar(x), Br(x) (r = 1, 2, 3) such that n s=1(Ps(x))2 = (A1(x))2 + (B1(x))2 = (A2(x))2 + x(B2(x))2 = (A3(x))2 −x(B3(x))2.