If two numbers have arithmetic mean 2700 and harmonic mean 75, then find their geometric mean.

Guest Dec 25, 2019

#1**+1 **

two numbers x and y

harmonic mean: ( 2/(1/x+1/y) )=75 re-arranging

2 (x * y)/(x+y) = 75

arithmetic mean :

(x+y)/2 = 2700 re-arranging

y = 5400- x sub this into red equation

2x(5400-x)/5400 = 75 re - arrange to

2 x^2 -10800x + 405000 = 0 Quadratic Formula shows x = 5362.24 and y = 37.76

Geometric mean: sqrt (x*y) =~ 450

(Thanx Guest for noticing my error....I have corrected this post)

ElectricPavlov Dec 25, 2019

#2**0 **

EP: Harmonic mean of 2 numbers is = 2 /{1/a + 1/b}

The answer should be: a≈37.7641 and b≈5362.24

Geometric mean = Sqrt{37.7641 x 5362.24} = 450

Guest Dec 25, 2019

#3**+1 **

You are CORRECT ! My mistake......I corrected my answer above.... Thanx! ~ EP

ElectricPavlov
Dec 25, 2019