`[(?)^2 + (16)^2 ) + 125 = 3.2`

Options

A. 11
B. 14
C. 16
D. None of these

Answer

To solve the equation \((?)^2 + (16)^2 + 125 = 3.2\), we will follow these steps:

### Step 1: Rewrite the equation
We start with the original equation:
\[ (?)^2 + 16^2 + 125 = 3.2 \]

### Step 2: Calculate \(16^2\)
Next, we calculate \(16^2\):
\[ 16^2 = 256 \]
Now, substitute this value back into the equation:
\[ (?)^2 + 256 + 125 = 3.2 \]

### Step 3: Combine like terms
Now, we combine \(256\) and \(125\):
\[ 256 + 125 = 381 \]
So, the equation now looks like this:
\[ (?)^2 + 381 = 3.2 \]

### Step 4: Isolate the square term
Next, we isolate \((?)^2\) by subtracting \(381\) from both sides:
\[ (?)^2 = 3.2 - 381 \]
Calculating the right side gives:
\[ 3.2 - 381 = -377.8 \]
Thus, we have:
\[ (?)^2 = -377.8 \]

### Step 5: Analyze the result
Since \((?)^2\) represents a square of a number, it must be non-negative (i.e., \((?)^2 \geq 0\)). However, we have found that \((?)^2 = -377.8\), which is negative. This indicates that there is no real number solution for the question mark.

### Conclusion
Therefore, the conclusion is that there is no value for the question mark that satisfies the equation.