SOLUTION: The product of two numbers is 5 and the sum of their reciprocals is 9/10. Find the numbers.

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Question 105453: The product of two numbers is 5 and the sum of their reciprocals is 9/10. Find the numbers.
Answer by checkley75(3666) About Me  (Show Source):
You can put this solution on YOUR website!
XY=5 OR X=5/Y
1/X+1/Y=9/10
NOW REPLACE X BY 5/Y & SOLVE FOR Y IN THE SECOND EQUATON.
1/(5/Y)+1/Y=9/10 NOW INVERT THE DENOMINATOR OF THE FIRST FRACTION.
Y/5+1/Y=9/10 NOW COMBINE THE FRACTIONS.
(Y*2+5)/5Y=9/10 NOW CROSS MULTIPLY
10Y^2+50=45Y
10Y^2-45Y+50=0
5(2Y^2-9Y+10)=0
5(2Y-5)(Y-2)=0
2Y-5=0
2Y=5
Y=5/2 OR 2.5 ANSWER
X*2.5=5
X=5/2.5
X=2 ANSWER.
PROOF
2*2.5=5
1/2.5+1/2=9/10
(5+4)/10=9/10
9/10=9/10