Which of the following is not a quadratic equation?

Options

A. `2(x-1)^(2)=4x^(2)-2x+1`
B. `2x-x^(2)=x^(2)+5`
C. `(sqrt(2)x+sqrt(3))^(2)=3x^(2)-5x`
D. `(x^(2)+2x)^(2)=x^(4)+3+4x^(2)`

Explanation

To determine which of the given options is not a quadratic equation, we need to analyze each option step by step. A quadratic equation is generally in the form of \( ax^2 + bx + c = 0 \), where \( a \neq 0 \).

### Step-by-Step Solution:

1. **Examine Option A:**
- The equation is given as \( (2x - 2)^2 = 4 \).
- Expanding the left side:
\[ (2x - 2)^2 = 4x^2 - 8x + 4 \]
- Setting the equation to zero:
\[ 4x^2 - 8x + 4 - 4 = 0 \implies 4x^2 - 8x = 0 \]
- This is a quadratic equation since the coefficient of \( x^2 \) is 4 (non-zero).

**Hint:** Check if the highest power of \( x \) is 2 and the coefficient is non-zero.

2. **Examine Option B:**
- The equation is \( 2x - x^2 = x^2 + 5 \).
- Rearranging gives:
\[ 2x - x^2 - x^2 - 5 = 0 \implies -2x^2 + 2x - 5 = 0 \]
- This can be rewritten as:
\[ 2x^2 - 2x + 5 = 0 \]
- This is also a quadratic equation since the coefficient of \( x^2 \) is 2 (non-zero).

**Hint:** Ensure that after rearranging, the highest degree term remains \( x^2 \) with a non-zero coefficient.

3. **Examine Option C:**
- The equation is \( \sqrt{2}x + \sqrt{3} = 3 \).
- Rearranging gives:
\[ \sqrt{2}x = 3 - \sqrt{3} \]
- Dividing by \( \sqrt{2} \):
\[ x = \frac{3 - \sqrt{3}}{\sqrt{2}} \]
- This equation does not contain an \( x^2 \) term, hence the coefficient of \( x^2 \) is 0.

**Hint:** Identify if the equation contains an \( x^2 \) term; if not, it is not a quadratic equation.

### Conclusion:
The option that is not a quadratic equation is **Option C**.