Answer:
Option A
Explanation:
To find the exact solutions of x^2 - 5x - 1 = 0, we can use the quadratic formula:
x = [-b ± sqrt(b^2 - 4ac)] / 2a
In this case, a = 1, b = -5, and c = -1. Substituting these values into the quadratic formula, we get:
x = [-(-5) ± sqrt((-5)^2 - 4(1)(-1))] / 2(1)
Simplifying inside the square root, we get:
x = [5 ± sqrt(25 + 4)] / 2
x = [5 ± sqrt(29)] / 2
Therefore, the exact solutions of x^2 - 5x - 1 = 0 are:
x = (5 + sqrt(29)) / 2
x = (5 - sqrt(29)) / 2