x1,x2,……,xn(自然数n>=3)为n个两两互不相等的实数.且x1+1/x2=x2+1/x3=……=xn+1/x1,求证x1^2*x2^2*……*xn^2=1
问题描述：
x1,x2,……,xn(自然数n>=3)为n个两两互不相等的实数.且x1+1/x2=x2+1/x3=……=xn+1/x1,求证x1^2*x2^2*……
*xn^2=1
答
x1+1/x2=x2+1/x3,得(x1-x2)=(x2-x3)/(x2*x3),x2+1/x3=x3+1/x4,得(x2-x3)=(x3-x4)/(x3*x4),.xn+1/x1=x1+1/x2,得(xn-x1)=(x1-x2)/(x1*x2),上面式子全部相乘,因为x1...xn两两不相等,左右可以同时消去(x1-x2)(x2-x3)...(...