Question

各位大哥大姐,啥也不说了,做题吧:已知a+1/a=4(0<a<1),求根号a-根号a分之1的值.(要过程)

Answer 1

a+1/a=(根号a-根号a分之1)的平方-1,即(根号a-根号a分之1)的值为正负根号下5

Answer 2

(SQR(a)-1/SQR(a))^2=a+1/a-2=4-2＝2
又因为0<a<1
所以SQR(a)-1/SQR(a)＝负根号2

Answer 3

a+1/a=4得， a^2+1=4a
令SQR(a)-1/SQR(a)=A
则A^2=(a^2+2a+1)/a=6a/a=6
SQR(a)-1/SQR(a)=正负根号6