Question

if arithmetic and geometric mean of two numbers are 8 and 7 respectively then find harmonic mean.​

Answer 1

Step-by-step explanation:

We know the relation between Arithmetic Mean, Harmonic Mean, and Geometric Mean of Two Numbers:

A.M. × H.M. = (G.M.)

2

⇒16× H.M. =8

2

⇒16× H.M. =64

⇒ H.M. =4

Answer 2

Answer:

harmonic mean = 6.125

Step-by-step explanation:

given arithmetic mean = 8

geometric mean = 7

let harmonic mean be 'x'

according to relation between AM GM and HM,

AM  * HM = (GM)^2

implies 8*x = 7^2

implies 8x = 49

therefore x = 49/8

that is x = 6.125

it proves that AM < GM < HM.