Final answer:
To solve the equation (√x + 2)(√x - 2) = 0, we set each factor equal to zero and solve for x. The solution is x = 4.
Step-by-step explanation:
To solve the equation (√x + 2)(√x - 2) = 0, we can use the zero product property which states that if the product of two factors is zero, then at least one of the factors must be zero. In this case, we have (√x + 2)(√x - 2) = 0, so we set each factor equal to zero.
Solving (√x + 2) = 0, we subtract 2 from both sides to obtain √x = -2. However, the square root of x cannot be negative, so there is no solution for this case.
Solving (√x - 2) = 0, we add 2 to both sides to obtain √x = 2. Squaring both sides, we get x = 4. So the solution to the equation (√x + 2)(√x - 2) = 0 is x = 4.
Learn more about Solving equations involving square roots