Best Answer

(x+y)/2=7; x+y=14; y=14-x

3=√(xy); xy=9; y=9/x

Use substitution:

14-x=9/x; 14x - x2=9; x2 - 14x +9=0

Use the quadratic formula:

x=[14±√(196-36)]/2; x=[14±√160]/2; x=[14±4√10]/2

x=7+2√10 or x=7-2√10

If x=7+2√10, then y=14-(7+2√10)=7-2√10

If x=7-2√10, then y=14-(7-2√10)=7+2√10

The first pair's geometric mean is √[(7+2√10)(7-2√10)]=√[72-(2√10)2]=√(49-40)=√9=3.

The first pair's arithmetic mean is (7+2√10 +7-2√10)/2=14/2=7

The second pair's geometric mean is √[(7-2√10)(7+2√10)]=√[72-(2√10)2]=√(49-40)=√9=3.

The second pair's arithmetic mean is (7-2√10 +7+2√10)/2=14/2=7

That's it!

Q: What are the 2 numbers if the arithmetic mean is 7 and the geometric mean is 3?

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Geometric mean of 2 and 12 is 4.898979485566356. Look at link: "Calculation of the geometric mean of two numbers".

The geometric mean of two numbers is the square root of their product. For example, the geometric mean of 4 and 25 is 10.

Geometric mean between 2 and 24 is 6.928203230275509. Look at link: "Calculation of the geometric mean of two numbers".

Neither.

The numbers are: 1-sqrt(2), 1 and 1+sqrt(2) or approximately -0.414214, 1 and 2.414214

Related questions

1.The Geometric mean is less then the arithmetic mean. GEOMETRIC MEAN < ARITHMETIC MEAN 2.

4

the arithmetic mean for the set of numbers is 7.4. but the geometric mean is 6.25826929.

The mean of the numbers a1, a2, a3, ..., an is equal to (a1 + a2 + a3 +... + an)/n. This number is also called the average or the arithmetic mean.The geometric mean of the positive numbers a1, a2, a3, ... an is the n-th roots of [(a1)(a2)(a3)...(an)]Given two positive numbers a and b, suppose that a< b. The arithmetic mean, m, is then equal to (1/2)(a + b), and, a, m, b is an arithmetic sequence. The geometric mean, g, is the square root of ab, and, a, g, b is a geometric sequence. For example, the arithmetic mean of 4 and 25 is 14.5 [(1/2)(4 + 25)], and arithmetic sequence is 4, 14.5, 25. The geometric mean of 4 and 25 is 10 (the square root of 100), and the geometric sequence is 4, 10, 25.It is a theorem of elementary algebra that, for any positive numbers a1, a2, a3, ..., an, the arithmetic mean is greater than or equal to the geometric mean. That is:(1/n)(a1, a2, a3, ..., an) ≥ n-th roots of [(a1)(a2)(a3)...(an)]

3mean is the average, so 2 + 4 = 6; 6 / 2 = 3* * * * *The above is the arithmetic mean which is NOT the same thing as the geometric mean.The geometric mean of n non-negative numbers is the nth root of their product.So GM(2, 4) = sqrt(8) = 2.828 (approx).

Geometric mean of 2 and 12 is 4.898979485566356. Look at link: "Calculation of the geometric mean of two numbers".

The geometric mean of two numbers is the square root of their product. For example, the geometric mean of 4 and 25 is 10.

Any two numbers can have only one arithmetic mean. If the numbers are x and y, then their arithmetic mean is (x + y)/2.

In a given sequence, there are two possible means calculatable: Arithmetic Mean, and Geometric Mean. The arithmetic mean, as we all know, is calculated from the sum of all the numbers divided by how many numbers there are: Sumn/n. The Geometric sum is calculated by multiplying all the numbers within the sequence together and taking the nth root of this value: (Productn)(1/n).In a geometric series, N(i)= a(ri), the geometric mean is found to be a(rn-1), where n is the number of elements within the series. this decreases or increases exponentially depending on the r value. If r1, increasing.Limitation Of Geometric Mean are:-1) Geometric mean cannot be computed when there are both negative and positive values in a series or more observations are having zero value.2)Compared to Arithmetic Mean this average is more difficult to compute and interpret.-Iwin

Geometric mean between 2 and 24 is 6.928203230275509. Look at link: "Calculation of the geometric mean of two numbers".

Its an arithmetic progression with a step of +4.

Neither.