设x1,x2.xn为互不相等的实数,且x1+1/x2=x2+1/x3=...=xn+1/x1 求证：x1²x2²...xn²=1
问题描述：
设x1,x2.xn为互不相等的实数,且x1+1/x2=x2+1/x3=...=xn+1/x1 求证：x1²x2²...xn²=1
答
∵x1＋1/x2＝x2＋1/x3,∴x1－x2＝1/x3－1/x2＝（x2－x3）/（x2x3）,∴x2x3＝（x2－x3）/（x1－x2）.······［1］∵x2＋1/x3＝x3＋1/x4,∴x2－x3＝1/x4－1/x3＝（x3－x4）/（x3x4）,∴x3x4＝（x3－x4）/（x2－x3...