A.M., G.M., H.M. and Their Relations
A.M., G.M., H.M. and Their Relations: Overview
This Topic covers sub-topics such as Relation between A.M., G.M. and H.M., AM-GM-HM Inequality, Relationship between Arithmetic Mean and Geometric Mean of Two Numbers and, Arithmetic Mean of mth Power Inequality
Important Questions on A.M., G.M., H.M. and Their Relations
If are positive real numbers whose product is a fixed number , the minimum value of is

If are positive real numbers whose product is a fixed number , the minimum value of is

If is the geometric mean of numbers , then what is the value of ?

Let and be positive real numbers such that . If the maximum value of is , then the value of is

Minimum value of is

If and then is necessarily.

If where, , then the minimum value of is:

The minimum value of where is

For a distinct complex numbers , the min value of

If are positive integers, then is

If are non-zero real numbers, then the minimum value of the expression equals

If , and is maximum, then

The sum of square of any real positive quantities and its reciprocal is never less

If is a unit vector and then maximum value of is

Find the number of real ordered pair(s) for which:

If A.M of two numbers is and their G.M. is , find the two numbers.

If A.M of two numbers be twice their G.M then the numbers are in the ratio.

For the two data points , find the relationship between AM, GM, HM, prove that, AM > GM > HM.

For the two data points , find the relationship between AM, GM, HM, prove that, AM > GM > HM.

Find the value of geometric mean GM, if the arithmetic mean AM is , and harmonic mean HM is .
