Asked by john
let the harmonic mean of two numbers x and y be 9.find the harmonic mean of the four numbers x,y,2x,2y
Answers
Answered by
Anoop
If x, y are in HP than 1/x, 1/y are in AP.
AM = (x+y)/2xy.
HM = 1/AM = 2xy/(x+y) = 9.
Similarly, AM = (1/x + 1/y + 1/2x + 1/2y)/4
AM = 3(x+y)/8xy
HM = 4*2xy/3(x+y) = 4/3 * 2xy/(x+y)
HM = 4/3 * 9 = 12
AM = (x+y)/2xy.
HM = 1/AM = 2xy/(x+y) = 9.
Similarly, AM = (1/x + 1/y + 1/2x + 1/2y)/4
AM = 3(x+y)/8xy
HM = 4*2xy/3(x+y) = 4/3 * 2xy/(x+y)
HM = 4/3 * 9 = 12
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.