`(?/31)xx(?/(279))=1`

Options

A. 31
B. 93
C. 217
D. 8649

Answer

To solve the equation \((?/31) \times (?/279) = 1\), we will follow these steps:

### Step 1: Rewrite the equation
We start with the equation:
\[ \frac{x}{31} \times \frac{x}{279} = 1 \]

### Step 2: Combine the fractions
We can combine the fractions on the left side:
\[ \frac{x \times x}{31 \times 279} = 1 \]
This simplifies to:
\[ \frac{x^2}{31 \times 279} = 1 \]

### Step 3: Cross-multiply
Next, we cross-multiply to eliminate the fraction:
\[ x^2 = 31 \times 279 \]

### Step 4: Calculate \(31 \times 279\)
Now we need to calculate \(31 \times 279\):
\[ 31 \times 279 = 8649 \]

### Step 5: Solve for \(x\)
We now have:
\[ x^2 = 8649 \]
To find \(x\), we take the square root of both sides:
\[ x = \sqrt{8649} \]

### Step 6: Simplify \(\sqrt{8649}\)
Next, we can factor \(8649\) to simplify the square root. We can start by finding the prime factors of \(8649\):
- \(8649\) is divisible by \(3\):
\[ 8649 \div 3 = 2883 \]
- \(2883\) is also divisible by \(3\):
\[ 2883 \div 3 = 961 \]
- \(961\) is \(31^2\) (since \(31 \times 31 = 961\)).

So, we can express \(8649\) as:
\[ 8649 = 3^2 \times 31^2 \]

### Step 7: Take the square root
Now we can take the square root:
\[ x = \sqrt{3^2 \times 31^2} = 3 \times 31 = 93 \]

### Conclusion
Thus, the value of \(x\) is:
\[ \boxed{93} \]