Q. 7

The product of three numbers in G.P. is 216. If 2, 8, 6 be added to them, the results are in A.P. Find the numbers.

Answer :

Let the three numbers be .


According to the question


…(1)


a3 = 216


a = 6


2,8,6 is added to them



The above sequence is in AP.


We know in AP.


2b = a + c



Substituting a = 6 in above equation we get,




28r = 6 + 6r2 + 8r


6r2 – 20r + 6 = 0


6r2 – 18r – 2r – 6 = 0


6r(r – 3) – 2(r – 3) = 0


(6r – 2) (r – 3) = 0


r = 3 or r = 1/3 .


Now the equation will be



2,6,18 or 18,6,2


The three numbers are 2,6,18.


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