Given:

Mean of a, b and 2 = 3

Standard deviation of a, b and 2 = 2/√3

To find:

Value of ab

Solution:

We know that,

Mean = (a + b + 2)/3 = 3

=> a + b = 7

Also, we know that,

Standard deviation = √[(a - mean)^2 + (b - mean)^2 + (2 - mean)^2]/√3 = 2/√3

Solving the above equation, we get,

(a - 3)^2 + (b - 3)^2 + 1 = 4/3

Expanding the above equation, we get,

a^2 + b^2 + 10 - 6a - 6b = 0

Now, we need to find the value of ab. For this, we can use the following formula,

(a - b)^2 = (a + b)^2 - 4ab

Substituting the value of a + b = 7, we get,

(a - b)^2 = 49 - 4ab

We can also expand (a - b)^2 as follows,

(a - b)^2 = a^2 + b^2 - 2ab

Substituting the value of a^2 + b^2 = 6a + 6b - 10, we get,

6a + 6b - 10 - 2ab = 49 - 4ab

Simplifying the above equation, we get,

4ab - 6a - 6b + 59 = 0

Now, we can solve the above equation to get the value of ab. One way to solve it is to use the quadratic formula,

ab = [6 ± √(6^2 - 4*4*59)]/8

Simplifying the above equation, we get,

ab = [3 ± √13]/2

Therefore, the value of ab is either (3 + √13)/2 or (3 - √13)/2.