已知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+(1/Xn)=Xn+(1/X1),求证X1^X2^...Xn……=1

问题描述:

已知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+(1/Xn)=Xn+(1/X1),求证X1^X2^...Xn……=1

楼主我来帮你解答吧首先看一个等式x1 +1/x2=x2 +1/x3所以x1-x2=1/x3-1/x2=(x2-x3)/(x2x3)即可得到x1-x2=(x2-x3)/(x2x3).x(n-1)-xn=(xn-x1)/(x1xn)xn-x1=(x1-x2)/(x1x2)n个等式相乘得到(x1x2...xn)^2=1要注意首尾消项...