2,
mathematical induction. If n = 1 the solutions are x = ±1, and if n = 2 the solutions are x = 0 and x = ± √
so in both cases the number of solutions is equal to n + 1. Suppose that the assertion holds for some n ∈ N .
Note that P n+2 (x) = P 2 (P n (x)) = P n 2 (x)(P n 2 (x) − 2), so the set of all real solutions of the equation P n+2 = 0 is
exactly the union of the sets of all real solutions of the equations P n (x) = 0, P n (x) = √
2 and P n (x) = − √
Bạn đang xem 2, - Đề thi Olympic sinh viên thế giới năm 2004
