What will come in place of both the question marks (?) in the following equation?
`(17 xx 32 div ? + 12)/(6^2 div 9 xx 4 - ?)`=10

Options

A. 16
B. 4
C. 8
D. 12

Answer

To solve the equation \((17 \times 32 \div ? + 12)/(6^2 \div 9 \times 4 - ?)=10\), we will follow these steps:

### Step 1: Simplify the equation
Let \( ? = x \). Then the equation becomes:
\[ \frac{(17 \times 32 \div x + 12)}{(6^2 \div 9 \times 4 - x)} = 10 \]

### Step 2: Calculate \(6^2\)
Calculate \(6^2\):
\[ 6^2 = 36 \]
Now substitute this back into the equation:
\[ \frac{(17 \times 32 \div x + 12)}{(36 \div 9 \times 4 - x)} = 10 \]

### Step 3: Simplify \(36 \div 9\)
Calculate \(36 \div 9\):
\[ 36 \div 9 = 4 \]
Now substitute this back into the equation:
\[ \frac{(17 \times 32 \div x + 12)}{(4 \times 4 - x)} = 10 \]

### Step 4: Calculate \(4 \times 4\)
Calculate \(4 \times 4\):
\[ 4 \times 4 = 16 \]
Now substitute this back into the equation:
\[ \frac{(17 \times 32 \div x + 12)}{(16 - x)} = 10 \]

### Step 5: Cross-multiply to eliminate the fraction
Cross-multiply:
\[ 17 \times 32 \div x + 12 = 10(16 - x) \]

### Step 6: Distribute on the right side
Distribute \(10\):
\[ 17 \times 32 \div x + 12 = 160 - 10x \]

### Step 7: Isolate the term with \(x\)
Rearranging gives:
\[ 17 \times 32 \div x + 10x = 160 - 12 \]
\[ 17 \times 32 \div x + 10x = 148 \]

### Step 8: Calculate \(17 \times 32\)
Calculate \(17 \times 32\):
\[ 17 \times 32 = 544 \]
Now substitute this back into the equation:
\[ \frac{544}{x} + 10x = 148 \]

### Step 9: Multiply through by \(x\) to eliminate the fraction
Multiply through by \(x\):
\[ 544 + 10x^2 = 148x \]

### Step 10: Rearrange into standard quadratic form
Rearranging gives:
\[ 10x^2 - 148x + 544 = 0 \]

### Step 11: Simplify the equation
Divide the entire equation by 2:
\[ 5x^2 - 74x + 272 = 0 \]

### Step 12: Use the quadratic formula
Use the quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\):
Here \(a = 5\), \(b = -74\), and \(c = 272\).
\[ b^2 - 4ac = (-74)^2 - 4 \times 5 \times 272 \]
Calculating \(b^2\):
\[ (-74)^2 = 5476 \]
Calculating \(4ac\):
\[ 4 \times 5 \times 272 = 5440 \]
Now calculate \(b^2 - 4ac\):
\[ 5476 - 5440 = 36 \]

### Step 13: Solve for \(x\)
Now substitute back into the quadratic formula:
\[ x = \frac{74 \pm \sqrt{36}}{10} \]
Calculating \(\sqrt{36}\):
\[ \sqrt{36} = 6 \]
So we have:
\[ x = \frac{74 \pm 6}{10} \]
Calculating the two possible values:
1. \(x = \frac{80}{10} = 8\)
2. \(x = \frac{68}{10} = 6.8\)

### Step 14: Verify the values
We need to check which of these values satisfy the original equation.

After checking, we find that \(x = 8\) satisfies the equation.

Thus, the value that comes in place of both the question marks is:
\[ \boxed{8} \]