Find the numbers the geometric mean of two numbers is 8 and their harmonic mean is 6.4

hikstac0 2022-09-09 Answered
Find the numbers the geometric mean of two numbers is 8 and their harmonic mean is 6.4
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

Elliott Rollins
Answered 2022-09-10 Author has 8 answers
Let the one number be a and as the geometric mean is 8, product of two numbers is 8 2 = 64 .
Hence, other number is 64 a
Now as harmonic mean of a and 64 a is 6.4,
it arithmetic mean of 1 a and a 64 is 1 6.4 = 10 64 = 5 32
hence, 1 a + a 64 = 2 × 5 32 = 5 16
and multiplying each term by 64a we get
64 + a 2 = 20 a
a 2 - 20 a + 64 = 0
a 2 - 16 a - 4 a + 64 = 0
a ( a - 16 ) - 4 ( a - 16 ) = 0
i.e. ( a - 4 ) ( a - 16 ) = 0
Hence a is 4 or 16.
If a=4, other number is 64 4 = 16 and if a=16, other number is 64 16 = 4
Hence numbers are 4 and 16,
Did you like this example?
Subscribe for all access

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in