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.

Explanation

Let the numbers are `a/r,a and ar.`

Then, `a/r*a*ar = 216`

`=>a^3 = 216 => a= 6`

Now, `2(a+8) = (a/r+2)+(ar+6)`

`=>2(6+8) = (6/r+2)+(6r+6)`

`=>28-6 = (6+2r)/r+6r`

`=>6r^2+2r-22r+6 = 0`

`=>6r^2-20r+6 = 0`

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