The difference between the square of two consecutive numbers is 47. The numbers are

Options

A. 24,25
B. 23, 24
C. 22, 23
D. 21, 22

Explanation

To solve the problem of finding two consecutive numbers whose squares differ by 47, we can follow these steps:

### Step 1: Define the Consecutive Numbers
Let the two consecutive numbers be \( n \) and \( n + 1 \).

### Step 2: Write the Equation for the Difference of Squares
The difference between the squares of these two numbers can be expressed as:
\[ (n + 1)^2 - n^2 \]

### Step 3: Expand the Squares
Now, expand the squares:
\[ (n + 1)^2 = n^2 + 2n + 1 \]
So, the difference becomes:
\[ (n^2 + 2n + 1) - n^2 = 2n + 1 \]

### Step 4: Set Up the Equation
According to the problem, this difference equals 47:
\[ 2n + 1 = 47 \]

### Step 5: Solve for \( n \)
Now, we will solve for \( n \):
1. Subtract 1 from both sides:
\[ 2n = 46 \]
2. Divide both sides by 2:
\[ n = 23 \]

### Step 6: Find the Two Consecutive Numbers
Now that we have \( n \), the two consecutive numbers are:
\[ n = 23 \quad \text{and} \quad n + 1 = 24 \]

### Step 7: Verify the Solution
To verify, we can check the difference of the squares:
\[ 24^2 - 23^2 = 576 - 529 = 47 \]
This confirms our solution is correct.

### Final Answer
The two consecutive numbers are **23 and 24**.

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