Question

The sum of natural number and its reciprocal s 65/8 find the number.
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Answer 1

Answer:

let's take a natural number = x

it's reciprocal = 1 / x

sum = 65 /8

x + 1 / x = 65 / 8

x2 + 1 / x = 65 / 8

8 ( x2 + 1) = 65 x

8 x2 + 8 = 65x

8 x2 - 65x + 8 = 0

let's factorize

8 x2 - 64x - x + 8 = 0

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

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

x - 8 = 0 or 8x -1 = 0

x = 8 or x = 1/8

check :

x + 1/x = 8 + 1/8 = (64 + 1) / 8 = 65/8