`(99)^2-(?)^2+(38)^2=8436`

Options

A. 57
B. 53
C. 49
D. 61

Answer

To solve the equation \( (99)^2 - (?)^2 + (38)^2 = 8436 \), we will follow these steps:

### Step 1: Calculate \( (99)^2 \) and \( (38)^2 \)

First, we need to calculate the squares of 99 and 38.

\[ (99)^2 = 9801 \]
\[ (38)^2 = 1444 \]

### Step 2: Substitute the values into the equation

Now, we substitute these values back into the equation:

\[ 9801 - (?)^2 + 1444 = 8436 \]

### Step 3: Combine the constants

Next, we combine the constants on the left side:

\[ 9801 + 1444 = 11245 \]

So the equation now looks like:

\[ 11245 - (?)^2 = 8436 \]

### Step 4: Isolate \( (?)^2 \)

Now, we isolate \( (?)^2 \) by subtracting 8436 from 11245:

\[ 11245 - 8436 = (?)^2 \]
\[ 2809 = (?)^2 \]

### Step 5: Take the square root

Finally, we take the square root of both sides to find the value of \( ? \):

\[ ? = \sqrt{2809} \]
\[ ? = 53 \]

Thus, the value that should replace the question mark is **53**.