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Question 1033393: answer these two questions.
1.)the sum of a number and its reciprocal is 5/2. find the number
2.) if a positive number is decreased by its reciproca,the result is 8/3.find the number.
Answer by addingup(3677)   (Show Source):
You can put this solution on YOUR website! Let x be the number.
x/1+1/x = 5/2 Here, x/1=x, so let's simplify:
x+1/x = 5/2
Multiply all terms times 2x:
2x^2+2 = 5x
Subtract 5x from both sides:
2x^2-5x+2 = 0
Factor the equation using FOIL:
(x-2)(2x-1)= 0
Split into 2 equations and solve for each:
x-2 = 0 or 2x-1 = 0
x = 2 or x = 1/2
Let's try the two possibilities to see which one is the correct answer:
2+1/2 = 4/2+1/2 = 5/2
Great, right off the bat I found the answer. Discard the other equation.
John
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