Three numbers whose sum is 18 are in AP if 2,4, 11 are added to them respective the resulting numbers are in GP. Find the numbers.

Explanation

Let the numbers are `a-r, a and a+r`.

Then,
`a+a-r+a+r = 18=> 3a = 18=> a = 6`

We are given if we add 2,4 and 11 to these numbers, it will be in GP.So,

`(6+4)/(6-r+2) = (6+r+11)/((6+4)`

`=>10/(8-r) = (17+r)/10`

`=> (17+r)(8-r) = 100`

`=>r^2+9r-136+100 = 0`

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