Final answer:
The value of 'a' in the geometric mean equation is 51.
Step-by-step explanation:
To find the value of 'a', we can use the formula for the geometric mean: √(a * 51) = 9√17. First, square both sides of the equation to eliminate the square root: a * 51 = (9√17)². Simplify the right side of the equation: a * 51 = 9² * (√17)². Since (√17)² = 17, we have: a * 51 = 9² * 17. Divide both sides of the equation by 51 to solve for 'a': a = (9² * 17) / 51. Calculate the right side of the equation: a = 3 * 17 = 51. Therefore, the value of 'a' is 51.