`(1.69xx1.69-0.23xx0.23)/(1.69-0.23) ="……………"`

Options

A. `1.46`
B. `14.6`
C. `1.92`
D. `19.2`

Answer

To solve the expression \((1.69 \times 1.69 - 0.23 \times 0.23) / (1.69 - 0.23)\), we can use the difference of squares identity, which states that \(a^2 - b^2 = (a + b)(a - b)\). Here's the step-by-step solution:

### Step 1: Identify \(a\) and \(b\)
Let \(a = 1.69\) and \(b = 0.23\).

### Step 2: Rewrite the expression using the difference of squares
We can rewrite the numerator \(1.69^2 - 0.23^2\) using the identity:
\[ 1.69^2 - 0.23^2 = (1.69 + 0.23)(1.69 - 0.23) \]

### Step 3: Substitute back into the expression
Now substitute this back into the original expression:
\[ \frac{(1.69 + 0.23)(1.69 - 0.23)}{1.69 - 0.23} \]

### Step 4: Cancel out the common terms
Since \(1.69 - 0.23\) appears in both the numerator and the denominator, we can cancel it out:
\[ 1.69 + 0.23 \]

### Step 5: Perform the addition
Now, we just need to add \(1.69\) and \(0.23\):
\[ 1.69 + 0.23 = 1.92 \]

### Final Answer
Thus, the final answer is:
\[ \boxed{1.92} \]

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