Solve this: Q If Geometric mean b/w a b is n times its harmonic mean then the - Maths - Sequences and Series

Question

Solve this:
Q If Geometric mean b/w a & b is n times its harmonic mean then
the value of a : b = ?

Brijendra Pal · Accepted Answer

Hi, GM between a and b = aband HM between a and b =2aba+baccording to the question, ab=n×2aba+bsquare, ab=n2×4ab×aba+b2a+b2=n2×4aba +b = 2nab
1a-b2 = a+b2-4ab = n2×4ab-4ab =4 n2-1aba-b =2 n2-1ab
2 adding equation 1 and 2 2a = 2nab+2abn2-1=2abn+n2-1a = abn+n2-1
3subtracting equation 1 and 2  , 2b=  2nab-2abn2-1=2abn-n2-1b = abn-n2-1
4so ab=abn+n2-1abn-n2-1=n+n2-1n-n2-1

Solve this: Q. If Geometric mean b/w a & b is n times its harmonic mean then the value of a : b = ?

Solve this:
Q. If Geometric mean b/w a & b is n times its harmonic mean then the value of a : b = ?