The value of `((2.697 - 0.498)^(2) + (2.697 + 0.498)^(2))/(2.697 xx 2.697 + 0.498 xx 0.498)` is

Options

A. 4
B. 2
C. 2.199
D. 3.195

Answer

To solve the expression \(\frac{(2.697 - 0.498)^{2} + (2.697 + 0.498)^{2}}{(2.697 \times 2.697) + (0.498 \times 0.498)}\), we can follow these steps:

### Step 1: Define the variables
Let:
- \( A = 2.697 \)
- \( B = 0.498 \)

### Step 2: Rewrite the expression
The expression can be rewritten as:
\[ \frac{(A - B)^{2} + (A + B)^{2}}{A^{2} + B^{2}} \]

### Step 3: Expand the numerator
Using the identity \((x - y)^{2} + (x + y)^{2} = 2x^{2} + 2y^{2}\), we can expand the numerator:
\[ (A - B)^{2} + (A + B)^{2} = 2A^{2} + 2B^{2} \]

### Step 4: Substitute back into the expression
Now, substituting this back into our expression, we have:
\[ \frac{2A^{2} + 2B^{2}}{A^{2} + B^{2}} \]

### Step 5: Simplify the expression
We can factor out the 2 from the numerator:
\[ = \frac{2(A^{2} + B^{2})}{A^{2} + B^{2}} \]

### Step 6: Cancel the common terms
Since \(A^{2} + B^{2}\) is common in the numerator and denominator (and not equal to zero), we can cancel it:
\[ = 2 \]

### Final Answer
Thus, the value of the given expression is:
\[ \boxed{2} \]