第49届国际数学奥林匹克数学竞赛题第2题是:(a)设实数x,y,z都不等于1,满足xyz=1,求证:(1-x2x)2+(1-y2y)2+(1-z2z)2≥1.(b)证明:存在无穷多组三元有理数组(x,y,z),x,y,z都不等于1,且xyz=1,使得上述不等式等号成立.经探讨发现,本题可拓展为定理1设正实数x,y,z满足kx,ky,kz都不等 The 49th International Mathematical Olympiad Competition Question 2 is: (a) Suppose that the real numbers x, y, z are not equal to 1 and satisfy xyz = 1, and prove: (1-x2x) 2+ (1-y2y) 2+ (1-z2z) 2≥1. (B) Prove that there are infinite sets of ternary rational arrays (x, y, z) where x, y and z are not equal to 1 and xyz = 1, Found that this issue can be extended to Theorem 1 Let positive real number x, y, z satisfy kx, ky, kz are not equal