Question

Find two numbers whose Arithmetic mean is 34 and geometric mean is 16 ​

Answer 1

Answer:

4 and 64

Step-by-step explanation:

let the numbers be a and b

given

arithmetic mean = (a+b)/2 = 34

a + b = 68.....(1)

geometric mean = 16

√ab = 16

ab = 16^2 = 256

now (a - b)^2 = (a + b)^2 - 4ab

= 68^2 - 4*256

= 68^2 - 32^2

= (68+32)(68-32)

= 100*36

= 3600

this gives

case 1

a - b = 60

a+b = 68 ..( from (1))

2a = 128

a = 64

b = 4

case 2

a - b = -60

a + b = 68

2a + 8

a = 4

b = 64

thus in both cases numbers are 4 and 64.

Answer 2

Answer:

4 and 64 are two numbers whose arithmetic mean is is 34 and geometric mean is 16.