Question 449996
Then why don't you?
 If you could solve this and get that answer, why can't you check it?
Perhaps you just copied the answer from the book?
 The easy solution is

1/a+1/b=
b/ab+a/ab
(a+b)/ab
10/20=.5
the harder way
a+b=10
ab=20

a=10-b
b*(10-b)=20
10b-b^2=20
b^2-10b+20=0
b^2-10b=-20

(b-5)^2=5
b = 5-sqrt(5)
b = 5+sqrt(5)
a+b=10

a = 5+sqrt(5)
a = 5-sqrt(5)

a = 5-sqrt(5)
b= 5+sqrt(5)

or 
b = 5-sqrt(5)
a = 5+sqrt(5)
so
1/a+1/b=
1/(5+sqrt(5))+1/(5-sqrt(5))


(5+sqrt(5))/ (5+sqrt(5))(5-sqrt(5))+(5-sqrt(5))/ (5+sqrt(5))(5-sqrt(5))
(5+sqrt(5)+5-sqrt(5))/(5+sqrt(5))(5-sqrt(5))
10/20=.5

(5+sqrt(5)(5-sqrt(5))=20