当A=2-√3时,求代数式1-2A+A²/A-1-√A²-2A+1/A²-A-1/A的值

题目

当A=2-√3时,求代数式1-2A+A²/A-1-√A²-2A+1/A²-A-1/A的值

答案

a=1/(2+√3)=2-√3
1-2a+a²/a-1 -√a²-2a+1/a²-a
=(a-1)²/a-1 -√(a-1)²/[a(a-1)]
=(a-1)+(a-1)/[a(a-1)]
=a-1+1/a
=2-√3-1+（2+√3)
=3