https://file.aiquickdraw.com/mathbot/file/17277293030339beck9sw.jpg

The equation in the image is:

\[
\sqrt{3a^2 - 3} - x = 0
\]

We are given \(x = 3\) and \(a > 0\). Let's solve for \(a\).

### Step 1: Substitute \(x = 3\) into the equation
\[
\sqrt{3a^2 - 3} - 3 = 0
\]

### Step 2: Add 3 to both sides
\[
\sqrt{3a^2 - 3} = 3
\]

### Step 3: Square both sides to eliminate the square root
\[
3a^2 - 3 = 9
\]

### Step 4: Add 3 to both sides
\[
3a^2 = 12
\]

### Step 5: Divide both sides by 3
\[
a^2 = 4
\]

### Step 6: Take the square root of both sides
\[
a = 2
\]

Since \(a > 0\), the solution is \(a = 2\).

Thus, the value of \(a\) is 2.

Would you like further details or explanations on any step?

Here are 5 related questions to expand on this concept:
1. How would the solution change if \(a\) could be negative?
2. What happens if you substitute \(x = 5\) instead of \(x = 3\)?
3. How would the problem change if the equation was \( \sqrt{3a^2 - 3} + x = 0 \)?
4. Can you solve a similar equation where the square root is on both sides, like \( \sqrt{3a^2 - 3} = \sqrt{9} \)?
5. How do you solve for \(a\) if the equation involved a cubic term, like \( \sqrt{3a^3 - 3} = 3 \)?

**Tip:** Always verify your solution by substituting the value of the variable back into the original equation to check for accuracy.

If a > 0 and x = 3 in the equation shown, what is the value of a? √(3a² - 3) - x = 0

Solve the equation √(3a² - 3) - x = 0 with the given condition x = 3 to find the value of a. This algebra problem involves concepts like square roots and solving quadratic-like equations. Suitable for students in Grades 9-11.

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