Question

若a=2-根号3 问：（1-2a+a²／a-1）-[（根号a²-2a+1）/a²-a]

Answer 1

∵a=2-√3,===>a-1=1-√3＜0.===>|a-1|=1-a.原式化简可得:原式=[(a-1)²/(a-1)]-[√(a-1)²/a(a-1)]=(a-1)-[|a-1|/a(a-1)]=(a-1)+[(1-a)/a(1-a)]=(a-1)+(1/a)=(1-√3)+1/(2-√3)=1-√3+2+√3=3.