Question

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

快
答案是三，不知道为什吗

为什吗a=2-√3,1/a=2+√3

Answer 1

解：∵a=2-√3,===>a-1=1-√3＜0.===>|a-1|=1-a.原式化简可得:原蔽咐式=[(a-1)²/(a-1)]-[√(a-1)²/a(a-1)]=(a-1)-[|a-1|/a(a-1)]=(a-1)+[(1-a)/宏慎纯a(1-a)]=(a-1)+(1/a)=(1-√3)+1/(2-√3)=1-√3+2+√孝销3=3.

Answer 2

（1-2a+a²／a-1）-[（棚如御根号a²链岩橡陵-2a+1）/a²-a]
=(1-a)^2/(a-1)-√(a-1)^2/a(a-1)
因a=2-√3,1/a=2+√3
a-1=1-√3<0
上式=a-1+1/a
=a-1+1/a
=1-√3+2+√3
=3

Answer 3

：（1-2a+a²／春姿a-1）-[（根号a²贺毕-2a+1）/a²-a]
=a-1-[-1/扒拍绝a]
=1-根号3+[2-根号3]=3