Let's call the two numbers x and y.
The arithmetic mean of x and y is defined as the sum of the two numbers divided by 2:
(x + y)/2 = 40
Multiplying both sides by 2, we get:
x + y = 80
The geometric mean of x and y is defined as the square root of their product:
sqrt(x*y) = 32
Squaring both sides, we get:
x*y = 32^2 = 1024
We now have two equations:
x + y = 80
x*y = 1024
We can use these equations to solve for x and y.
One way to do this is to use substitution. Rearrange the first equation to solve for one of the variables in terms of the other:
x + y = 80
y = 80 - x
Substitute this expression for y in the second equation:
x*y = 1024
x*(80 - x) = 1024
Expanding the left side, we get:
80x - x^2 = 1024
Rearranging terms and setting equal to zero, we get a quadratic equation:
x^2 - 80x + 1024 = 0
We can solve for x using the quadratic formula:
x = [80 +/- sqrt(80^2 - 411024)] / 2
x = [80 +/- sqrt(384)] / 2
x = [80 +/- 16sqrt(6)] / 2
x = 40 +/- 8sqrt(6)
We get two solutions for x:
x = 40 + 8sqrt(6) ≈ 66.66
or
x = 40 - 8sqrt(6) ≈ 13.34
We can use either of these values to solve for y using the equation y = 80 - x:
If x = 40 + 8sqrt(6):
y = 80 - x = 80 - (40 + 8sqrt(6)) = 40 - 8sqrt(6) ≈ 13.34
If x = 40 - 8sqrt(6):
y = 80 - x = 80 - (40 - 8sqrt(6)) = 40 + 8sqrt(6) ≈ 66.66
Therefore, the two numbers are approximately 13.34 and 66.66.
The difference between arithmetic and geometric mean you can find in the following link: "Calculation of the geometric mean of two numbers".
The difference between arithmetic and geometric mean you can find in the following link: "Calculation of the geometric mean of two numbers".
Two numbers: 3.2 and 4: Geometric mean is 3.5777087639996634 Arithmetic mean is 3.6 Scroll down to related links and look at "Geometric and Arithmetic Mean".
You can find the differences between arithmetic and geometric mean in the following link: "Calculation of the geometric mean of two numbers".
The difference between arithmetic and geometric mean you can find in the following link: "Calculation of the geometric mean of two numbers".
The differences between arithmetic and geometric mean you can find in the following link: "Calculation of the geometric mean of two numbers". Cheers ebs
You can find the differences between arithmetic and geometric mean in the following link: "Calculation of the geometric mean of two numbers". Cheers ebs
An arithmetic-geometric mean is a mean of two numbers which is the common limit of a pair of sequences, whose terms are defined by taking the arithmetic and geometric means of the previous pair of terms.
You can see the difference in the following link: "Calculation of the geometric mean of two numbers".
1.The Geometric mean is less then the arithmetic mean. GEOMETRIC MEAN < ARITHMETIC MEAN 2.
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The geometric mean, if it exists, is always less than or equal to the arithmetic mean. The two are equal only if all the numbers are the same.