Final answer:
Solving the quadratic equation x² - 3x + 1 = 0 using the quadratic formula gives us solutions x = (3 + √5)/2 and x = (3 - √5)/2. Option D is closest to these solutions, but no exact match is provided in the choices, which could indicate an error in the answer choices.
Step-by-step explanation:
To solve the quadratic equation x² - 3x + 1 = 0 using the quadratic formula, we must first identify the coefficients a, b, and c from the standard form of a quadratic equation, which is ax²+bx+c = 0. In this case:
Next, we apply these values to the quadratic formula: x = (-b ± √(b²-4ac))/(2a). Performing the calculations, we have:
x = (-(-3) ± √((-3)²-4(1)(1)))/(2(1))
x = (3 ± √(9-4))/(2)
x = (3 ± √(5))/(2)
Therefore, the solutions to the equation are x = (3 + √5)/2 and x = (3 - √5)/2. Since none of the answer choices provided exactly match these solutions, and the question seems to have typos, it's likely that the correct answer choice is meant to be similar to these solutions.
Looking through the provided options, the only one that closely resembles the correct solution is D. (3 + 5)/2, although this is not an exact match since √5 is not equal to 5. It seems there may be an error in the answer choices if none exactly match the solution obtained from using the quadratic formula.