Answer:
To find the original three numbers, let's first consider the ratio they are in: 1:2:3. Let's call the three numbers in the ratio as x, 2x, and 3x.
Next, we are told that when 2, 4, and 11 are added to these numbers respectively, the resulting numbers form a geometric progression (G.P).
In a G.P, each term is obtained by multiplying the previous term by a constant value called the common ratio (r).
Let's say the common ratio is r.
Based on this information, we can write the equations:
(x + 2) = x * r
(2x + 4) = (x + 2) * r
(3x + 11) = (2x + 4) * r
Now, we can solve these equations to find the value of x and the common ratio r.
Expanding the equations, we have:
x + 2 = xr
2x + 4 = xr + 2r
3x + 11 = 2xr + 4r
Rearranging the equations, we get:
xr - x = 2
2xr - x - 2r = 0
2xr - 3x + 4r - 11 = 0
Now, we can solve these equations simultaneously using any suitable method, such as substitution or elimination, to find the values of x and r.
Once we have the values of x and r, we can find the original three numbers by substituting them back into the expressions x, 2x, and 3x.
Please note that the values of x and r may not always be whole numbers or integers.
Explanation:
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