To solve this problem, let's assume that the natural number is represented by the variable "x".
According to the problem, the natural number is doubled when added to its reciprocal. Mathematically, this can be expressed as:
2x + 1/x
To find the value of "x", we can set up the equation and solve for it.
2x + 1/x = x
To solve this equation, we can multiply through by "x" to eliminate the denominator:
2x^2 + 1 = x^2
Rearranging the terms:
2x^2 - x^2 + 1 = 0
x^2 + 1 = 0
This equation has no real solutions, which means that there is no natural number that satisfies the condition. Therefore, the correct answer is option C) 1.
Option A) 1/2 - This option is incorrect because the reciprocal of 1/2 is 2, and when added to 1/2, it does not result in doubling the number.
Option B) 2 - This option is incorrect because when 2 is added to its reciprocal (1/2), it does not result in doubling the number.
Option C) 1 - This option is correct because when 1 is added to its reciprocal (1/1 = 1), it does result in doubling the number.
Option D) 0 - This option is incorrect because when 0 is added to its reciprocal (which is undefined), it does not result in doubling the number.