Final answer:
If a-2/a = 5, the value of a is C. 4.
Step-by-step explanation:
To solve the equation a-2/a = 5 and find the value of a, we can start by multiplying both sides of the equation by a to eliminate the fraction.
This gives us a(a-2/a) = 5a. Simplifying further, we get a^2 - 2 = 5a.
Now, we can move all the terms to one side of the equation to get a quadratic equation: a^2 - 5a - 2 = 0.
Using factoring, the quadratic equation can be factored as (a - 4)(a + 1) = 0.
Thus, the possible values for a are a = 4 and a = -1.
However, since a negative value for a would result in a fraction in the initial equation, we can conclude that the value of a is 4.
Therefore the correct answer is C. 4.