`(?)^(2)+15^(2)-33^(2)=97`

Options

A. 33
B. 32
C. 34
D. None of these

Explanation

To solve the equation \((?)^2 + 15^2 - 33^2 = 97\), we can follow these steps:

### Step 1: Rewrite the equation
Let \( x \) represent the question mark. The equation can be rewritten as:
\[ x^2 + 15^2 - 33^2 = 97 \]

### Step 2: Calculate \( 15^2 \) and \( 33^2 \)
Calculate the squares of 15 and 33:
\[ 15^2 = 225 \]
\[ 33^2 = 1089 \]

### Step 3: Substitute the squares back into the equation
Now substitute these values back into the equation:
\[ x^2 + 225 - 1089 = 97 \]

### Step 4: Simplify the equation
Combine the constants on the left side:
\[ x^2 + 225 - 1089 = 97 \]
\[ x^2 - 864 = 97 \]

### Step 5: Move the constant to the right side
Add 864 to both sides:
\[ x^2 = 97 + 864 \]
\[ x^2 = 961 \]

### Step 6: Take the square root of both sides
Now take the square root of both sides to solve for \( x \):
\[ x = \sqrt{961} \]

### Step 7: Calculate the square root
The square root of 961 is:
\[ x = 31 \]

### Final Answer
Thus, the value of the question mark is:
\[ \boxed{31} \]

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