Final answer:
The equation x² - 8x + 16 = 1 is solved by recognizing (x-4)² as a perfect square, applying the square root property to both sides, and solving for x, giving two solutions: x = 5 and x = 3.
Step-by-step explanation:
The student asked how to solve the equation using the square root property: x² - 8x + 16 = 1. To solve this equation, we first recognize that the left-hand side is a perfect square. Specifically, (x-4)² = x² - 8x + 16. Therefore, we can write the equation as (x-4)² = 1.
Next, we apply the square root property, which allows us to take the square root of both sides, giving us x-4 = ±√1. This simplifies to x-4 = ±1. Finally, we solve for x and find two potential solutions, x = 4 + 1 and x = 4 - 1, which simplifies to x = 5 and x = 3 respectively.
In conclusion, the correct answers are x = 5 and x = 3, which corresponds to options b) and c) from the given choices.