已知:xy=1,x=2+根号3,求x+1分之1+y-1分之1的值
问题描述：
已知:xy=1,x=2+根号3,求x+1分之1+y-1分之1的值
答
1/(x+1)+1/(y-1)
=1/(x+1)+1/(1/x-1)
=1/(x+1)+x/(1-x)
=[1-x+x(x+1)]/(1-x^2)
=(1+x^2)/(1-x^2)
=(1+4+4根号3+3)/(1-4-4根号3-3)
=(8+4根号3)/(-6-4根号3)
=-(4+2根号3)/(3+2根号3)
=-(4+2根号3)(3-2根号3)/(9-12)
=(12-2根号3-12)/3
=-2根号3/3