SOLUTION: Find two numbers whose product is 3 and the difference of whose reciprocals is 1/6. thank you

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Question 937583: Find two numbers whose product is 3 and the difference of whose reciprocals is 1/6. thank you
Answer by MathTherapy(10552) About Me  (Show Source):
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Find two numbers whose product is 3 and the difference of whose reciprocals is 1/6. thank you


Let smaller number be S

Then larger is: 3%2FS

Smaller number's reciprocal: 1%2FS

Larger number's reciprocal:  1%2F%283%2FS%29, or S%2F3

Difference of their reciprocals equals 1%2F6, so: 1%2FS+-+S%2F3+=+1%2F6

6+-+2S%5E2+=+S ----- Multiplying by LCD, 6S

2S%5E2+%2B+S+-+6+=+0

(2S - 3)(S + 2) = 0

2S = 3                OR             S + 2 = 0

S, or smaller number = system%28%283%2F2%29_or%2C-+2%29



If smaller number is: 3%2F2, then larger number is: 3%2F%283%2F2%29, or 3%282%2F3%29, or 2. 

Thus, numbers CAN BE: highlight_green%28system%28%283%2F2%29_and%2C2%29%29



If smaller number is: -+2, then larger number is: 3%2F-+2%29, or -+3%2F2 

Thus, numbers CAN BE: highlight_green%28system%28-+2_and%2C-+3%2F2%29%29