Final answer:
Given options (A, B, C, D) are correct. To solve the equation 3d² + 8 = 6 for all real solutions, we isolate the quadratic term, solve for d², and take the square root.
Step-by-step explanation:
To solve the equation 3d² + 8 = 6 for d, we first isolate the d² term:
Subtract 8 from both sides: 3d² = -2.
Divide both sides by 3: d² = -2/3.
In this case, the equation does not have any real solutions because we cannot take the square root of a negative number within the system of real numbers. Therefore, there are no real solutions to this equation, and none of the given options (A, B, C, D) are correct.
To solve the equation 3d² + 8 = 6, we first subtract 8 from both sides to isolate the quadratic term:
3d² = -2
Then, we divide both sides by 3 to solve for d²:
d² = -2/3
Finally, we take the square root of both sides to solve for d:
d = ±√(-2/3)
As the square root of a negative number is not a real number, there are no real solutions to this equation. Therefore, the correct answer is None of the above.