Question

已知a=根号2- 1，化简求值

a-1分之a平方-1-a的平方-a分之根号a的平方-2a+1-a分之1

Answer 1

解：∵a=√2-1<0，
∴a-1<0，
(a^2-1)/(a-1)-√(a^2-2a+1)/(a^2-a)-1/a
=(a+1)-|a-1|/a(a-1)-1/a
=(a+1)+1/a-1/a
=a+1
∴当a=√2-1时，
原式=√2。

Answer 2

=(a+1)(a-1)/(a-1) -√(a-1)²/a(a-1) -1/a
=a+1 +1/a-1/a
=a+1
=√2