Question

先化简再求值:a-1分之1-2a+a平方-a的平方-2a+1其中a+-根号3

Answer 1

解：原式=（a-1）^2/(a-1)-根号下（a-1）^2/a(a-1)
=a-1-根号下（a-1）^2/a(a-1)
当a=根号3时，a-1>0，根号下（a-1）^2=a-1
a-1-根号下（a-1）^2/a(a-1)
=a-1-(a-1)/a(a-1)
=a-1-1/a
=根号3-1-1/根号3
=2/3根号3-1
当a=-根号3时，a-1<0，根号下（a-1）^2=1-a
a-1-根号下（a-1）^2/a(a-1)
=a-1-(1-a)/a(a-1)
=a-1+1/a
=根号3-1+1/根号3
=4/3根号3-1

Answer 2

解：原式=(1-a)²/(a-1)-√(1-a)²/a(a-1)
当a=√3时，
(1-a)²/(a-1)-√(1-a)²/a(a-1)
=（√3-1）-1/√3
=√3-1-√3/3
=2√3/3-1
当a=-√3时，
(1-a)²/(a-1)-√(1-a)²/a(a-1)
=-（√3+1）+1/√3
=-（2√3/3+1）