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 The Twentieth Canadian Mathematical Olympiads 1988年第二十届加拿大数学奥林匹克 For what real values of k do 1988x2 + kx + 8891 and 8891x2 + kx + 1988 have a common zero ? Given a triangle area A and perimeter p, let S be the set of all points a distance 5 or less from a point of the triangle. Find the area of S . Given n > 4 points in the plane, some of which are colored red and the rest black. No three points of the same color are collinear. Show that we can find three points of the same color, such that two of the points do not have a point of the opposite color on the segment joining them . Define two integer sequences a0, a1, a2, ... and b0, b1, b2, ... as follows. a0 = 0, a1 = 1, an+2 = 4an+1 - an, b0 = 1, b1 = 2, bn+2 = 4bn+1 - bn. Show that bn2 = 3an2 + 1 . If S is a sequence of positive integers let p(S) be the product of the members of S. Let m(S) be the arithmetic mean of p(T) for all non-empty subsets T of S. S' is formed from S by appending an additional positive integer. If m(S) = 13 and m(S') = 49, find S' . 点击此处查看相关视频讲解 在方框内输入单词或词组