The A.M. of two given positive numbers is 2. If the larger number is increased by 1, the G.M. of the numbers becomes equal to the A.M. of the given numbers. Then find the H.M.

Answer

`3/2`

Explanation

Let a,b`(agtb)` be the two numbers. Given,
`(a+b)/2=2` or a+b=4 (1)
and `sqrt((a+1)b)=2`
or (a+1)b=4
or `b^(2)-5b+4=0` [Using (1)]
or b=1,4
But `bne4`, therefore, b=1, and hence a=3.
Hence, harmonic mean,
`H=(2xx3xx1)/(3+1)=3/2`