Question

The difference of an integer and its reciprocal is 143 12
. Find the
integer

Answer 1

Answer:

Let the integer be k.

Given that k-\frac{1}{k}

k

1

=143/12

Taking LCM and cross multiplying, we get

12k^{2}k

2

-12=143k

12k^{2}k

2

-143k-12=0

This is a quadratic equation.

12k^{2}k

2

-144k+k-12=0

12k(k-12)+(k-12)=0

(k-12)(12k+1)=0

k=12,\frac{-1}{12}

12

−1

Since k is an integer, therefore k=12

Hope the solution is clear to you.

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Explanation:

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