Answer:

Given: AM = 5, GM = 4

Let the two observations be a and b.

Then, we have:

AM = (a + b)/2 = 5

GM = sqrt(ab) = 4

Squaring both sides of the second equation, we get:

ab = 16

Substituting this in the first equation, we get:

a + b = 10

Now, we need to find two numbers whose sum is 10 and product is 16. These numbers are 2 and 8.

Therefore, the two observations are 2 and 8.

Explanation:

Arithmetic Mean (AM) is the average of two observations. It is calculated by adding the two values and dividing by 2.

Geometric Mean (GM) is the square root of the product of two observations.

In this question, we are given the values of AM and GM, and we need to find the two observations. Using the formulas for AM and GM, we can write two equations and solve for the two unknown values.

We start by assuming that the two observations are a and b. We then use the formulas for AM and GM to write two equations in terms of a and b. We then simplify the equations and solve for a and b.

In this case, we have two equations and two unknowns, so we can solve for the values of a and b. Once we have the values of a and b, we can verify that they satisfy the conditions given in the question.