What approximate value will come in place of questions mark (?) in the given questions? (You are not expected to calculate the exact value.)
`(1.99+5.02)^2-(1+?)=10.93xx3.05`

Options

A. 11
B. 19
C. 15
D. 7

Answer

To solve the equation \( (1.99 + 5.02)^2 - (1 + ?) = 10.93 \times 3.05 \) and find the approximate value of \( ? \), we can follow these steps:

### Step 1: Simplify the left-hand side
First, we approximate \( 1.99 \) and \( 5.02 \):
- \( 1.99 \approx 2 \)
- \( 5.02 \approx 5 \)

So, we can rewrite the expression:
\[ (1.99 + 5.02)^2 \approx (2 + 5)^2 = 7^2 = 49 \]

### Step 2: Calculate the right-hand side
Next, we approximate \( 10.93 \) and \( 3.05 \):
- \( 10.93 \approx 11 \)
- \( 3.05 \approx 3 \)

Now we can calculate:
\[ 10.93 \times 3.05 \approx 11 \times 3 = 33 \]

### Step 3: Set up the equation
Now, we can substitute our approximations back into the equation:
\[ 49 - (1 + ?) \approx 33 \]

### Step 4: Rearrange the equation
Rearranging gives us:
\[ 49 - 1 - ? \approx 33 \]
\[ 48 - ? \approx 33 \]

### Step 5: Solve for ?
Now we can solve for \( ? \):
\[ -? \approx 33 - 48 \]
\[ -? \approx -15 \]
Thus,
\[ ? \approx 15 \]

### Conclusion
The approximate value of \( ? \) is \( 15 \).