`((63+36)^(2)+(63-36)^(2))/(63^(2)+36^(2))` =?

Options

A. 1
B. 2
C. 3
D. 4

Answer

To solve the expression \(\frac{(63+36)^2 + (63-36)^2}{63^2 + 36^2}\), we will follow these steps:

### Step 1: Calculate \(63 + 36\) and \(63 - 36\)
First, we compute the values of \(63 + 36\) and \(63 - 36\):
\[ 63 + 36 = 99 \]
\[ 63 - 36 = 27 \]

### Step 2: Calculate \((63 + 36)^2\) and \((63 - 36)^2\)
Now we square these results:
\[ (63 + 36)^2 = 99^2 = 9801 \]
\[ (63 - 36)^2 = 27^2 = 729 \]

### Step 3: Add the squares together
Next, we add these two squares:
\[ (63 + 36)^2 + (63 - 36)^2 = 9801 + 729 = 10530 \]

### Step 4: Calculate \(63^2\) and \(36^2\)
Now we calculate \(63^2\) and \(36^2\):
\[ 63^2 = 3969 \]
\[ 36^2 = 1296 \]

### Step 5: Add \(63^2\) and \(36^2\)
Now we add these two results:
\[ 63^2 + 36^2 = 3969 + 1296 = 5265 \]

### Step 6: Divide the results
Finally, we divide the sum of the squares from Step 3 by the sum of the squares from Step 5:
\[ \frac{(63 + 36)^2 + (63 - 36)^2}{63^2 + 36^2} = \frac{10530}{5265} \]

### Step 7: Simplify the fraction
Now we simplify \(\frac{10530}{5265}\):
\[ \frac{10530}{5265} = 2 \]

Thus, the final answer is:
\[ \boxed{2} \]