If the harmonic mean between two positive numbers is to their geometric mean as 12:13. The numbers are in the ratio
14:19
By the given condition if the numbers be a and b then
2aba+b:√ab=12:13
2√aba+b=1213
26√ab=12(a+b).
Divisible by 2b
⇒13√ab=6(ab+1) put √ab=x6x2−13x+6=0 ∴(2x−3)(3x−2)=0⇒x=32 or 23=√ab
∴ab=94 or 49
Hence, the numbers are in the ratio 4:9