SOLUTION: The sum of the reciprocals of two numbers is 14. The difference of their reciprocals is 4. Find the 2 numbers

Question 561242: The sum of the reciprocals of two numbers is 14. The difference of their reciprocals is 4. Find the 2 numbers
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
The sum of the reciprocals of two numbers is 14. The difference of their reciprocals is 4. Find the 2 numbers
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Let x, y be the two numbers
Given: sum of the reciprocals is 14, the difference of the reciprocals is 4
1/x + 1/y = 14
1/x - 1/y = 4
Add the two equations:
2/x = 18
x = 2/18 = 1/9
Solve for y:
1/y = 14 - 1/x
1/y = 14 - 9 = 5
y = 1/5
So the numbers are 1/5 and 1/9
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