Question

已知a+b等于6,ab等于4,求根号a加根号b分之根号a减根号b

Answer 1

设根号a=A,根号b＝B

则A^2+B^2=6,A^2B^2=4,AB=2

所有为：（A-B)/(A+B)

(A-B)^2=A^2-2AB+B^2=6-4=2

(A+B)^2=A^2+2AB+B^2=6+4=10

(A-B)^2/(A+B)^2=2/10=1/5

开方得：

(A-B)/(A+B)=根号5/5