If (3-x)+(6)+(7+5x) is a G.P.Find two possible values for x,common ratio,sum of the g.p.

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If (3-×)+6+(7-3×) is a Gp.find the two possible values for x

To find possible values for x, common ratio, and the sum of the geometric progression (G.P.), we need to simplify the expression given.

The expression is: (3-x) + 6 + (7 + 5x)

Step 1: Combine the terms inside the parentheses.
The expression becomes:
9 - x + 6 + 7 + 5x

Step 2: Combine like terms.
Combine the constants and the terms with "x":
22 + 4x

Now, we have the simplified expression: 22 + 4x.

To identify whether this expression represents a geometric progression, we need to check if the coefficients of x form a constant ratio. In this case, the coefficient of x is 4, which is constant.

Therefore, the expression 22 + 4x can be considered a geometric progression.

Now, let's find the possible values of x, common ratio, and the sum of the geometric progression.

To find the possible values of x:
There are infinitely many possible values for x since x can be any real number. It is not possible to narrow it down to one or two specific values without additional information or restrictions.

To find the common ratio:
Since the expression 22 + 4x is a linear equation and not a geometric progression, we cannot determine a common ratio.

To find the sum of the geometric progression:
Since we couldn't determine the common ratio for this expression, we cannot calculate the sum of the geometric progression.

In summary:
- There are infinitely many possible values for x.
- There is no common ratio since the expression is not a geometric progression.
- The sum of the geometric progression cannot be determined.

If the terms are a GP, then

6/(3-x) = (7+5x)/6
36 = 21 + 15x - 7x - 5x^2
5x^2 - 8x +15 = 0

This quadratic has no real solution, thus the terms are not a GP in the set of real numbers.

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