The value of `((14)^2 - (7)^2times2)/(7times4) = ?`

Options

A. 98
B. 35
C. 350
D. None of these.

Answer

To solve the equation \(\frac{(14)^2 - (7)^2 \times 2}{7 \times 4}\), we will follow these steps:

### Step 1: Calculate \( (14)^2 \) and \( (7)^2 \)
First, we need to calculate the squares of 14 and 7.

\[ (14)^2 = 196 \]
\[ (7)^2 = 49 \]

### Step 2: Substitute the values into the equation
Now we substitute these values back into the equation:

\[ \frac{196 - (49 \times 2)}{7 \times 4} \]

### Step 3: Calculate \( 49 \times 2 \)
Next, we calculate \( 49 \times 2 \):

\[ 49 \times 2 = 98 \]

### Step 4: Substitute and simplify the numerator
Now substitute this back into the equation:

\[ \frac{196 - 98}{7 \times 4} \]

### Step 5: Calculate \( 196 - 98 \)
Now, we perform the subtraction in the numerator:

\[ 196 - 98 = 98 \]

### Step 6: Calculate \( 7 \times 4 \)
Next, we calculate the denominator:

\[ 7 \times 4 = 28 \]

### Step 7: Substitute and simplify
Now substitute these values into the equation:

\[ \frac{98}{28} \]

### Step 8: Simplify the fraction
Now we simplify the fraction:

\[ \frac{98}{28} = 3.5 \]

### Final Answer
Thus, the value of the expression is:

\[ \boxed{3.5} \]