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If the Arithmetic mean between two numbers is 64 and the Geometric mean between them is 16. The Harmonic Mean between them is ______________.
- a)64
- b)4
- c)16
- d)40
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
If the Arithmetic mean between two numbers is 64 and the Geometric mea...
Answer:
The harmonic mean is =4
Explanation:Let the 2
numbers be a and b
Then,
Most Upvoted Answer
If the Arithmetic mean between two numbers is 64 and the Geometric mea...
Solution:
Let the two numbers be x and y. Then we have:
Arithmetic mean = (x + y)/2 = 64
Geometric mean = √(xy) = 16
To find the Harmonic mean, we use the formula:
Harmonic mean = 2/(1/x + 1/y)
= 2xy/(x + y)
Calculation:
Substituting the given values, we get:
x + y = 128 (from Arithmetic mean)
xy = 256 (from Geometric mean)
Substituting these values in the formula for Harmonic mean, we get:
Harmonic mean = 2xy/(x + y)
= 2 × 256/128
= 4
Therefore, the Harmonic mean between the two numbers is 4. Thus, option (B) is correct.
Let the two numbers be x and y. Then we have:
Arithmetic mean = (x + y)/2 = 64
Geometric mean = √(xy) = 16
To find the Harmonic mean, we use the formula:
Harmonic mean = 2/(1/x + 1/y)
= 2xy/(x + y)
Calculation:
Substituting the given values, we get:
x + y = 128 (from Arithmetic mean)
xy = 256 (from Geometric mean)
Substituting these values in the formula for Harmonic mean, we get:
Harmonic mean = 2xy/(x + y)
= 2 × 256/128
= 4
Therefore, the Harmonic mean between the two numbers is 4. Thus, option (B) is correct.
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Community Answer
If the Arithmetic mean between two numbers is 64 and the Geometric mea...
We know, AM = a+b/2
GM = √ab
and, HM = 2/(1/a + 1/b)
Now, AM = 64 and GM = 16
Then, HM = 1/64 × 16² = 4
GM = √ab
and, HM = 2/(1/a + 1/b)
Now, AM = 64 and GM = 16
Then, HM = 1/64 × 16² = 4
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