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The Sum of a Positive Number and Its Reciprocal is Thrice the Difference of the Number and Its Reciprocal. The Number is?

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Explanation

The sum of a positive number and its reciprocal is thrice.

The difference of the number and its reciprocal.

The number will be figure out in this way.

Let suppose the positive number is y.

The difference of a number and its reciprocal

y – 1/y

The sum of a positive number and its reciprocal

y + 1/y = 3(y – 1/y) ________ (i)

Through equation (i) we can easily find out the value of y (y = 2 square root).

To Find

Number = ?

Solution

Let suppose

Number = y

According to the given condition

y + 1/y = 3(y – 1/y)

y + 1/y = 3y – 3/y

1/y + 3/y = 3y – y

1 + 3 = y(3y – y)

4 = 3y2 – y2

2y2 = 4

y2 = 2

y = 2 square root

Required Number = 2 square root answer

Conclusion

The sum of a positive number and its reciprocal is thrice the difference of the number and its reciprocal. The number is 2 square root.

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