Question

The arithmetic mean (A) of two numbers (a and b) is given by the formula A=a+b/2 , and their geometric mean (G) is given by G=root ab . Their harmonic mean (H) is given by the formula H=root AH . Which formula correctly gives H in terms of a and b?

Answer 1

The answer is simply: H=2ab/a+b

Answer 2

Answer:

Hence, formula which  correctly gives H in terms of a and b is:

           $\dfrac{2ab}{a+b}$

Step-by-step explanation:

If x1,x2,...xn are n observations then harmonic mean is given by:

$\dfrac{n}{\dfrac{1}{x1}+\dfrac{1}{x2}+...\dfrac{1}{xn}}$

 Here, we are given two observations a and b

Hence, harmonic mean is:

 $\dfrac{2}{\dfrac{1}{a}+\dfrac{1}{b}} \\\\\\=\dfrac{2ab}{a+b}$

Hence, formula which  correctly gives H in terms of a and b is:

           $\dfrac{2ab}{a+b}$