Find three number in G.P. whose sum is 38 and their product is 1728.

Solution:

Let the three numbers be ,
According to the question,
eq.(1)
eq.(2)
From eq.(2) we obtain,

From eq.(1) we obtain,


On substituting in eq.(3) we obtain


By dividing eq.(4) by 2 we obtain

The eq. will now be

Therefore the terms are
As a result, the three numbers are