Question 290858: The sum of a number and its reciprocal is 10/3 . what is the number? Also need to know how to check it.Thank you a bunch! Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! The sum of a number and its reciprocal is 10/3 . what is the number? Also need to know how to check it.Thank you a bunch!
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Equation:
x + 1/x = 10/3
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Multiply thru by 3x to get:
3x^2 + 3 = 10x
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Rearrange:
3x^2 - 10x + 3 = 0
Factor:
3x^2 - 9x - x + 3 = 0
3x(x-3)-(x-3) = 0
(x-3)(3x-1) = 0
Positive solution:
x = 1/3
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Checking:
x + (1/x) = 10/3
(1/3) + 3 = 10/3
(1/3)+(9/3) = 10/3
10/3 = 10/3
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Cheers,
stan H.
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