Question

If the A.M. of two numbers exceeds their G.M. by 2 and their H.M. by 18/5
find the numbers.​

Answer 1

Step-by-step explanation:

Given  

If the A.M. of two numbers exceeds their G.M. by 2 and their H.M. by 8/5 find the numbers.

Let the two numbers be a and b

Now A = G + 2

G = h + 8/5

H = G – 8/5

G^2 = AM

G^2 = AM

       = (G + 2) (G – 8/5)

G^2 = G^2 + 2G – 8G/5 – 16/5

2G = 8G/5 + 16/5

2G/5 = 16/5

2G = 16

G = 8

G^2 = 64

Now ab = 64 So b = 64/a

A = G + 2

So a + b / 2 = 10

So a + b = 20

Now a + 64/a = 20

Now a^2 – 20 a + 64 = 0

 So a^2 – 16 a – 4 a + 64 = 0

Now a(a – 16) – 4(a – 16) = 0

So (a – 16) (a – 4) = 0

So a = 16 , a = 4

If a = 16, b = 64 / 16

         Now b = 4

If a = 4, b = 64 / 4

Now b = 16

So a = 16, b = 4 and a = 4, b = 16