Question

Which of the following options represents the real roots of the given power equation: 3(x - 4)³ + 16 = 64?

A. x = 12 and x= -4
B. x= 12
C. x= -4
D. x= -12 and x= 4

Answer 1

The real root of the equation 3(x - 4)³ + 16 = 64 is found to be x = 6 after simplifying the equation and taking the cube root. This correct answer is not listed in the provided options.

Step-by-step explanation:

To find the real roots of the power equation 3(x - 4)³ + 16 = 64, we need to simplify and solve for x:

• First, subtract 16 from both sides to get 3(x - 4)³ = 48.
• Divide both sides by 3 to isolate the cubic term, giving us (x - 4)³ = 16.
• Take the cube root of both sides, which simplifies to x - 4 = 2 since the cube root of 16 is 2.
• Finally, add 4 to both sides to solve for x, resulting in x = 6.

Since the equation has a single power of ³ (cubic) and we have found one real root, there are no other changes in signs or factors that would result in additional real roots. Therefore, the correct answer is B. x= 6, which is not listed in the incorrect multiple-choice options provided. The other options do not satisfy the original equation.