What value will come in place of question mark (?) in the questions given below?
`? = [ (26 (6.5)^2 + 1)/((7.5)^2 - 7.5 xx 2)]`

Options

A. `(2850)/(225)`
B. `2958/225`
C. `2718/215`
D. None of these

Answer

To solve the equation given in the question, we will follow these steps:

**Step 1: Calculate \( (6.5)^2 \)**
First, we need to find the square of 6.5.
\[ (6.5)^2 = 6.5 \times 6.5 = 42.25 \]

**Step 2: Calculate \( 26 \times (6.5)^2 + 1 \)**
Now, we will multiply 26 by the result from Step 1 and then add 1.
\[ 26 \times 42.25 + 1 = 1098.5 + 1 = 1099.5 \]

**Step 3: Calculate \( (7.5)^2 \)**
Next, we need to find the square of 7.5.
\[ (7.5)^2 = 7.5 \times 7.5 = 56.25 \]

**Step 4: Calculate \( 7.5 \times 2 \)**
Now, we will multiply 7.5 by 2.
\[ 7.5 \times 2 = 15 \]

**Step 5: Calculate the denominator \( (7.5)^2 - 7.5 \times 2 \)**
Now, we will subtract the result from Step 4 from the result from Step 3.
\[ 56.25 - 15 = 41.25 \]

**Step 6: Divide the results from Step 2 by Step 5**
Now we will divide the result from Step 2 by the result from Step 5.
\[ \frac{1099.5}{41.25} \]

**Step 7: Simplify the division**
To simplify, we can multiply both the numerator and denominator by 100 to eliminate the decimals.
\[ \frac{109950}{4125} \]

**Step 8: Perform the division**
Now, we will perform the division.
\[ 109950 \div 4125 = 26.67 \quad \text{(approximately)} \]

Thus, the value that comes in place of the question mark (?) is approximately **26.67**.

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