SOLUTION: Two numbers have a sum of 5, and the sum of their reciprocals is 1. Find the exact numbers.

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Question 1046746: Two numbers have a sum of 5, and the sum of their reciprocals is 1. Find the exact numbers.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
system%28x%2By=5%2C1%2Fx%2B1%2Fy=1%29

y=5-x
-
%28y%2Bx%29%2Fxy=1
x%2By=xy
x%2B5-x=x%285-x%29
5=5x-x%5E2
-x%5E2%2B5x-5=0
x%5E2-5x%2B5=0

x=%285%2B-+sqrt%2825-4%2A5%29%29%2F2

x=%285%2B-+sqrt%285%29%29%2F2

y=5-x
for the x with PLUS,
y=5-%285%2Bsqrt%285%29%29%2F2
y=10%2F2-%285%2Bsqrt%285%29%29%2F2
y=%2810-5-sqrt%285%29%29%2F2
y=%285-sqrt%285%29%29%2F2


The two numbers are %285-sqrt%285%29%29%2F2 and %285%2Bsqrt%285%29%29%2F2.