a=二分之根号5加1,b=二分之根号5减1,求a+b/1+b/1+a(a+b)/b的值.

题目

a=二分之根号5加1,b=二分之根号5减1,求a+b/1+b/1+a(a+b)/b的值.

答案

1/(a+b)+1/b+b/a(a+b)
=(ab+a^2+ab+b^2)/ab(a+b)
=(a+b)^2/ab(a+b)
=(a+b)/ab
=[(√5+1)/2+(√5-1)/2]/[(√5+1)/2*(√5-1)/2]
=(√5)/[(5-1)/4]
=(√5)/(4/4)
=√5