The solution for b is b=±√ac/9. Option a is the correct choice.
We begin by dividing both sides of the equation by 9b²c to isolate b:
a / (9b²c) = 1
Simplifying the left side, we get:
a/9b² = 1/c
Taking the square root of both sides, we obtain:
√(a/9b²) = √(1/c)
Simplifying the left side and solving for b, we find:
√(ac)/9b = 1/c
b = ±√ac/9
Therefore, the solutions to the equation a=9b²c are:
b = ±√ac/9
Note that both positive and negative values of b satisfy the equation.
Option a is the correct choice.