Question

The sum of an integer and its reciprocal is 145/12 . Find the integers

Answer 1

Answer:

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Answer 2

Answer:

Let the required integer be x.

Then ,

The reciprocal of the integer = 1/x.

According to the question;

The sum of the integer and its reciprocal is 145/12.

=> x + 1/x = 145/12

=> (x^2 + 1)/x = 145/12

=> 12(x^2 + 1) = 145x

=> 12x^2 + 12 = 145x

=> 12x^2 - 145x + 12 = 0

=> 12x^2 - 144x - x + 12 = 0

=> 12x(x - 12) - (x - 12) = 0

=> (x - 12)(12x - 1) = 0

=> x = 12 , 1/12

Since, x must be an integer , thus the appropriate value of x is 12.

Hence, the required integer is 12.