Final answer:
To solve the equation x - (1/x) = 35/6, we can multiply both sides of the equation by 6 to eliminate the fraction. This gives us the equation 6x^2 - 35x - 6 = 0. Solving this quadratic equation, we find that the number is 1/2 or 0.5.
Step-by-step explanation:
To solve this problem, let's assume the number is represented by 'x'. The reciprocal of the number would be represented by '1/x'. According to the given information, the difference between the number and its reciprocal is 35/6.
So, we can set up the equation x - (1/x) = 35/6. To solve this equation, we need to get rid of the fraction. Multiplying both sides of the equation by 6 gives us 6x - 6(1/x) = 35. Simplifying further, we get 6x - 6/x = 35.
To eliminate the fraction, we can multiply both sides of the equation by x, resulting in 6x^2 - 6 = 35x. Rearranging the equation, we have 6x^2 - 35x - 6 = 0.
Now we can solve this quadratic equation by factoring or using the quadratic formula. In this case, factoring the equation gives us (2x - 1)(3x + 6) = 0. Setting each factor equal to zero, we find that x = 1/2 or x = -2.
Since the question asks for a positive number, the answer is x = 1/2. Therefore, the number is 1/2 or 0.5.