Question

1/(6k²) = 1/(3k²) - 1/4
A. k = -1
B. k = 1/2
C. k = 2
D. k = -2

Answer 1

The equation 1/(6k²) = 1/(3k²) - 1/4 is solved by finding a common denominator, eliminating the fractions, and isolating the variable k. The result is that k = ±sqrt(2)/3, which does not match any of the provided options.

Step-by-step explanation:

The student is asking to solve the algebraic equation 1/(6k²) = 1/(3k²) - 1/4. To find the value of k that satisfies this equation, let's proceed with the following steps:

1. Combine the terms on the right side of the equation by finding a common denominator, which would be 12k².
2. After combining the terms, rewrite the equation as (2 - 6k²)/(12k²) = 1/(4).
3. Multiply both sides of the equation by 12k² to eliminate the fractions.
4. After simplification, the equation becomes 2 - 6k² = 3k².
5. Combine like terms to get 9k² = 2.
6. Finally, divide both sides by 9 to solve for k², resulting in k² = 2/9.
7. Take the square root of both sides to find k = ±sqrt(2/9), which simplifies to k = ±sqrt(2)/3.

The correct answer is not listed among the options A, B, C, or D, so there may be an error in the question or the provided options.