SOLUTION: if ab=1 and a+b= 3' then find a and b.

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Question 903062: if
ab=1
and a+b= 3'
then find a and b.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
a%2Bb=3
ab=1
Then,
a=1%2Fb
Substituting,
1%2Fb%2Bb=3
1%2Bb%5E2=3b
b%5E2-3b%2B1=0
Complete the square.
b%5E2-3b%2B9%2F4%2B1=9%2F4
%28b-3%2F2%29%5E2=9%2F4-4%2F4
%28b-3%2F2%29%5E2=5%2F4
b-3%2F2=0+%2B-+sqrt%285%29%2F2
b=3%2F2+%2B-+sqrt%285%29%2F2
So then,
a%2B%283%2F2+%2B-+sqrt%285%29%2F2%29=3
a=-3%2F2+%2B-+sqrt%285%29%2F2
Remember that the +/- symbol changes from a to b
so if a=-3%2F2+%2B+sqrt%285%29%2F2 then b=3%2F2+-+sqrt%285%29%2F2