Final answer:
To solve the quadratic inequality x² - 8x + 1 < 0, we find the roots of the quadratic equation x² - 8x + 1 = 0 and determine the range of x between the roots.
Step-by-step explanation:
To solve the quadratic inequality x² - 8x + 1 < 0, we can first find the roots of the quadratic equation x² - 8x + 1 = 0. Using the quadratic formula, we get:
x = (8 ± √(64 - 4(1)(1))) / 2
x = (8 ± √(60)) / 2
x = (8 ± 2√15) / 2
x = 4 ± √15
Since the inequality is less than zero, we need to find when x is between the roots of the equation. Therefore, the solution set for the quadratic inequality is:
x ∈ (4 - √15, 4 + √15)