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levacccp [35]
4 years ago
6

The sum of a number and its reciprocal is 65/8. Find the numbers.

Mathematics
1 answer:
djyliett [7]4 years ago
8 0

Answer: 8 and \frac{1}{8}

<u>Step-by-step explanation:</u>

x + \frac{1}{x} = \frac{65}{8}

need to eliminate the denominator:

x(8x) + \frac{1}{x}(8x) = \frac{65}{8}(8x)

8x² + 8 = 65x

8x² - 65x + 8 = 0

(8x -1)(x - 8) = 0

(8x -1) = 0           (x - 8) = 0

x = \frac{1}{8}                      x = 8

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