SOLUTION: URGENT QUESTION .. HELP NEEDED the question is- the difference between a positive fraction and its reciprocal is 9/20 find the sum of that fraction and its reciprocal. Thank

Algebra ->  Inverses -> SOLUTION: URGENT QUESTION .. HELP NEEDED the question is- the difference between a positive fraction and its reciprocal is 9/20 find the sum of that fraction and its reciprocal. Thank      Log On


   

Question 209223: URGENT QUESTION .. HELP NEEDED
the question is-
the difference between a positive fraction and its reciprocal is 9/20
find the sum of that fraction and its reciprocal.
Thanks. a lot
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
x = the number
1/x is the reciprocal of the number
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x - (1/x) = 9/20
multiply both sides by x to get:
x^2 - 1 = (9/20)*x
subtract (9/20)*x from each side of the equation to get:
x^2 - (9/20)*x - 1 = 0
multiply both sides of the equation by 20 to get:
20x^2 - 9x - 20 = 0
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using the quadratic formula of %28-b+%2B-+sqrt%28b%5E2-4ac%29%29%2F%282a%29 gets me:
x = 50/40
or:
x = -32/40
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x = -32/40 is rejected because it is not positive and the problem stated that it had to be a positive fraction.
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your answer is x = 50/40 which is the same as:
x = 5/4
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to confirm this answer is correct, substitute in the original equations.
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if we let x = 5/4, then:
x - (1/x) = 9/20 becomes:
%285%2F4%29+-+%281%2F%285%2F4%29%29+=+9%2F20
this is the same as:
%285%2F4%29+-+%284%2F5%29+=+9%2F20
this becomes:
%2825-16%29%2F20+=+9%2F20
which becomes:
9%2F20+=+9%2F20 confirming that x = 5/4 is good.
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your question was:
find the sum of the fraction and it's reciprocal.
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the answer is:
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if x = 5/4, then 1/x = 4/5 and the sum is 5/4 + 4/5 = (25+16)/20 = 41/20
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