Question

Find arithmetic mean of two positive numbers whose geometric mean and harmonic mean are 4 and 16/5 respectively

Answer 1

Answer:

G^2=AH

4^2=A*16/5

16=A*16/5

16(5/16)=A

5=A

A=5

Answer 2

Answer:

5

Step-by-step explanation:

Let say two numbers are  

A  & B

to find AM  = (A + B)/2

GM = √AB  = 4

=> AB = 16

HM = 2/(1/A + 1/B)  = 16/5

=> 2AB/( B + A)  = 16/5

=> 5AB / 16 = (A + B)/2

=> 5 * 16 / 16 = (A + B)/2

=>  (A + B)/2 = 5

arithmetic mean of two positive numbers whose geometric mean and harmonic mean are 4 and 16/5 respectively  = 5

Additional info

AB = 16

A + B = 10

=> x² - 10x + 16 = 0

=> x = 2 & 8

numbers are  2  &  8