Final answer:
The solutions to the equation (x - 4)² = 5 are found by taking the square root of both sides and solving for x. The solutions are 4 + √5 and 4 - √5, so the correct answer is a. 4 ± √5.
Step-by-step explanation:
To find the solutions to the equation (x − 4)² = 5, we need to take the square root of both sides of the equation. This will give us two possible solutions for x because a square root can be both positive and negative.To find the solutions to the equation (x − 4)² = 5,
we can take the square root of both sides of the equation. (x − 4)² = 5 can be rewritten as x − 4 = ±√5. Solving for x, we have x = 4 ± √5. Therefore, the solutions to the equation are a. 4 ± √5.First, compute the square root of 5:√5Then, since we have (x − 4)², we set x − 4 equal to ±5:x − 4 = ±√5Now, solve for x by adding 4 to both sides:x = 4 + √x = 4 − √5Therefore, the correct answer to the given equation is a. 4 ± √5.