Question

已知;a=2+根号3分之一,求a-1分之1-2a+a²-a²-a分之根号a²-2a+1的值

Answer 1

a=1/(2+√3)

=(2-√3)/[(2-√3)(2+√3)]

=(2-√3)/(2²-√3²)

=(2-√3)/(4-3)

=2-√3

1/a=2+√3

原式=[ (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=2-√3-1=1-√3﹤0

∴原式=a-1+{ (a-1)/[a(a-1)] }

=a-1+(1/a)

=2-√3-1+2+√3

=3