If x = 2 and m = 3 , the equation is `3x^(2) - 2kx + 2m = 0` , find k .

Answer

To solve the equation \(3x^2 - 2kx + 2m = 0\) for \(k\) given that \(x = 2\) and \(m = 3\), we can follow these steps:

### Step 1: Substitute the values of \(x\) and \(m\) into the equation.
We start with the equation:
\[ 3x^2 - 2kx + 2m = 0 \]
Substituting \(x = 2\) and \(m = 3\):
\[ 3(2)^2 - 2k(2) + 2(3) = 0 \]

### Step 2: Calculate \(3(2)^2\) and \(2(3)\).
Calculating \(3(2)^2\):
\[ 3(2^2) = 3(4) = 12 \]
Calculating \(2(3)\):
\[ 2(3) = 6 \]

### Step 3: Substitute these values back into the equation.
Now substituting these values back into the equation gives us:
\[ 12 - 4k + 6 = 0 \]

### Step 4: Combine like terms.
Combine \(12\) and \(6\):
\[ 18 - 4k = 0 \]

### Step 5: Solve for \(k\).
To isolate \(k\), we can rearrange the equation:
\[ -4k = -18 \]
Dividing both sides by \(-4\):
\[ k = \frac{18}{4} = \frac{9}{2} \]

### Conclusion:
Thus, the value of \(k\) is:
\[ k = \frac{9}{2} \]