Question

One-eighth of a positive number is twice its
reciprocal. What is the number?
Answer is 4, but don't know which formula to use.​

Answer 1

Step-by-step explanation:

The equation in the question is not correct, assuming the wording of the question is correct. It should be

2/x - x = -23/5

Can you solve for x and finish from here? Hint: Multiply both sides by 5x, get a quadratic equation in x, solve it, and keep only the positive root.

Answer 2

Step-by-step explanation:

Let the number be x

Reciprocal of a number = 1x\frac{1}{x}

x

1

We are given that The sum of a positive number and its reciprocal is twice the difference of the number and its reciprocal

So, x+1x=2(x−1x)x+\frac{1}{x}=2(x-\frac{1}{x})x+

x

1

=2(x−

x

1

)

x+1x=2x−2xx+\frac{1}{x}=2x-\frac{2}{x}x+

x

1

=2x−

x

2

2x+1x=2x−x\frac{2}{x}+\frac{1}{x}=2x-x

x

2

+

x

1

=2x−x

3x=x\frac{3}{x}=x

x

3

=x

3=x23=x^23=x

2

3=x\sqrt{3}=x

3

=x

Hence the number is 3\sqrt{3}

3

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