`(3.65xx3.65+2.35xx2.35-2xx2.35xx3.65)/1.69=?`

Options

A. 1.69
B. 2.35
C. 3.65
D. 1

Answer

To solve the expression \((3.65 \times 3.65 + 2.35 \times 2.35 - 2 \times 2.35 \times 3.65) / 1.69\), we can follow these steps:

### Step 1: Identify the components of the expression
We have:
- \(A = 3.65\)
- \(B = 2.35\)

The expression can be rewritten as:
\[ A^2 + B^2 - 2AB \]

### Step 2: Recognize the formula
The expression \(A^2 + B^2 - 2AB\) is the expansion of \((A - B)^2\). Thus, we can rewrite the expression as:
\[ (3.65 - 2.35)^2 \]

### Step 3: Calculate \(3.65 - 2.35\)
Now, let's calculate:
\[ 3.65 - 2.35 = 1.30 \]

### Step 4: Substitute back into the expression
Now we substitute back:
\[ (1.30)^2 \]

### Step 5: Calculate \((1.30)^2\)
Calculating \(1.30 \times 1.30\):
\[ 1.30 \times 1.30 = 1.69 \]

### Step 6: Substitute into the division
Now we substitute this result into the original expression:
\[ \frac{1.69}{1.69} \]

### Step 7: Simplify the expression
Now we simplify:
\[ \frac{1.69}{1.69} = 1 \]

### Final Answer
Thus, the final answer is:
\[ \boxed{1} \]

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