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

 Dec 25, 2019
 #1
avatar+19806 
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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)

 Dec 25, 2019
edited by ElectricPavlov  Dec 25, 2019
edited by ElectricPavlov  Dec 26, 2019
 #2
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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

 Dec 25, 2019
 #3
avatar+19806 
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You are CORRECT !   My mistake......I corrected my answer above....  Thanx!    ~ EP     cheeky

ElectricPavlov  Dec 25, 2019

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