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Relation between arithmetic and Geometric mean of two numbers a and b (a > b) is A.M. = 2 G.M. Find the ratio between numbers.
- a)√3+1 :(√3-1)
- b)2+√3 :2-√3
- c)√5+1 :√5-1
- d)can’t determine
Correct answer is option 'B'. Can you explain this answer?
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Relation between arithmetic and Geometric mean of two numbers a and b ...
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Relation between arithmetic and Geometric mean of two numbers a and b ...
The arithmetic mean (AM) and geometric mean (GM) are two ways to calculate the average of two numbers, a and b.
The arithmetic mean is calculated by adding the two numbers together and dividing by 2:
AM = (a + b) / 2
The geometric mean is calculated by taking the square root of the product of the two numbers:
GM = √(a * b)
There is a relationship between the arithmetic mean and the geometric mean known as the AM-GM inequality. It states that for any two positive numbers a and b, the arithmetic mean is always greater than or equal to the geometric mean:
AM ≥ GM
In other words, the arithmetic mean is always greater than or equal to the geometric mean of two positive numbers.
This inequality is useful in various mathematical proofs and applications. It can also be extended to more than two numbers.
The arithmetic mean is calculated by adding the two numbers together and dividing by 2:
AM = (a + b) / 2
The geometric mean is calculated by taking the square root of the product of the two numbers:
GM = √(a * b)
There is a relationship between the arithmetic mean and the geometric mean known as the AM-GM inequality. It states that for any two positive numbers a and b, the arithmetic mean is always greater than or equal to the geometric mean:
AM ≥ GM
In other words, the arithmetic mean is always greater than or equal to the geometric mean of two positive numbers.
This inequality is useful in various mathematical proofs and applications. It can also be extended to more than two numbers.
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Relation between arithmetic and Geometric mean of two numbers a and b (a > b) is A.M. = 2 G.M. Find the ratio between numbers.a)√3+1 :(√3-1)b)2+√3 :2-√3c)√5+1 :√5-1d)can’t determineCorrect answer is option 'B'. Can you explain this answer?
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