The value of `[((0.337+0.126)^(2)-(0.337-0.126)^(2))/(0.337xx0.126)]` is

Options

A. `4`
B. `0.211`
C. `0.463`
D. `0.4246`

Answer

To solve the expression \(\frac{(0.337 + 0.126)^2 - (0.337 - 0.126)^2}{0.337 \times 0.126}\), we can use the difference of squares formula, which states that \(a^2 - b^2 = (a - b)(a + b)\).

### Step-by-Step Solution:

1. **Identify \(a\) and \(b\)**:
Let \(a = 0.337 + 0.126\) and \(b = 0.337 - 0.126\).

2. **Calculate \(a\) and \(b\)**:
\[ a = 0.337 + 0.126 = 0.463 \]
\[ b = 0.337 - 0.126 = 0.211 \]

3. **Apply the difference of squares formula**:
\[ (0.463)^2 - (0.211)^2 = (0.463 - 0.211)(0.463 + 0.211) \]

4. **Calculate \(0.463 - 0.211\) and \(0.463 + 0.211\)**:
\[ 0.463 - 0.211 = 0.252 \]
\[ 0.463 + 0.211 = 0.674 \]

5. **Multiply the results**:
\[ (0.463)^2 - (0.211)^2 = 0.252 \times 0.674 \]

6. **Calculate \(0.252 \times 0.674\)**:
\[ 0.252 \times 0.674 = 0.169848 \]

7. **Calculate \(0.337 \times 0.126\)**:
\[ 0.337 \times 0.126 = 0.042462 \]

8. **Divide the results**:
\[ \frac{0.169848}{0.042462} \approx 4.0 \]

### Final Answer:
The value of \(\frac{(0.337 + 0.126)^2 - (0.337 - 0.126)^2}{0.337 \times 0.126}\) is approximately \(4.0\).