If geometric mean and harmonic mean of two numbers a and b are 16 and 64/5 respectively, then the value of a: b is

Step-by-step solution

Geometric mean of a and b= a b a b =16 (given) a b=256 ....(i) And harmonic mean of a and b= 2 a b a+b 2 a b a+b = 64 5 (given) 2 256 a+b = 64 5 [from Eq. (i)] 2 a b a+b = 64 5 (given) 2 256 a+b = 64 5 [from Eq. (i)] a+b=40 ....(ii) Now, (a-b)= (a+b)^2-4 a b = (40)^2-4 256 = 1600-1024 = 576 a-b=24 ....(iii) On solving Eqs. (ii) and (iii), we get a=32 and b=8 a: b=32: 8=4: 1