SOLUTION: If a+b=10 and ab=20 Find the value of 1/a + 1/b I ended up with a 0.5, but I'm not entirely sure and I'd love to cross check!

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Question 449996: If a+b=10 and ab=20
Find the value of 1/a + 1/b
I ended up with a 0.5, but I'm not entirely sure and I'd love to cross check!
Answer by rwm(914) About Me  (Show Source):
You can put this solution on YOUR website!
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