例1(第31届西班牙数学奥林匹克试题)已知(x+x2+1)(y+y2+1)=1,求证:x+y=0.笔者也曾关注过这道西班牙竞赛题,并查阅了关于此题的一些解法,最近又看到贵刊也谈及此题,更激起了笔者的兴趣.经过研究,笔者发现用三角代换可证明此竞赛题及其变式,现给出解法与大家一起探讨.证明众所周? Example 1 (the 31st Spanish Mathematical Olympiad Question) is known as (x+x2+1)(y+y2+1)=1, and verification: x+y=0. The author has also paid attention to this Spanish competition question, and Check out some of the solutions to this problem, and recently I saw that your magazine also talked about this topic, which further stimulated the author’s interest. After researching, the author found that using trigonal substitution can prove this competition title and its variants. Exploring the solution to explore with everyone.