The solution of the set `{x:x inR, x^(2)=9,2x=9}` is an empty set .

Answer

To determine the solution of the set \( \{x : x \in \mathbb{R}, x^2 = 9, 2x = 9\} \), we will analyze each equation separately.

### Step 1: Solve the equation \( x^2 = 9 \)

To solve \( x^2 = 9 \), we take the square root of both sides:

\[ x = \pm 3 \]

So, the solutions from this equation are:

\[ x = 3 \quad \text{and} \quad x = -3 \]

### Step 2: Solve the equation \( 2x = 9 \)

Now, we solve the second equation \( 2x = 9 \):

\[ x = \frac{9}{2} = 4.5 \]

### Step 3: Find the intersection of the solutions

Now we have two sets of solutions:

1. From \( x^2 = 9 \): \( \{3, -3\} \)
2. From \( 2x = 9 \): \( \{4.5\} \)

Next, we need to find the intersection of these two sets:

\[ \{3, -3\} \cap \{4.5\} \]

Since there are no common elements between these two sets, the intersection is:

\[ \emptyset \]

### Conclusion

Thus, the solution of the set \( \{x : x \in \mathbb{R}, x^2 = 9, 2x = 9\} \) is indeed an empty set.

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