If `sqrt(x) - (1)/(sqrt(x)) = 2sqrt(2)`, then `x^(2) + (1)/(x^(2))` is equal to :

Options

A. 102
B. 98
C. 104
D. 100

Answer

To solve the equation \( \sqrt{x} - \frac{1}{\sqrt{x}} = 2\sqrt{2} \) and find the value of \( x^2 + \frac{1}{x^2} \), we can follow these steps:

### Step 1: Isolate the square root expression
We start with the equation:
\[ \sqrt{x} - \frac{1}{\sqrt{x}} = 2\sqrt{2} \]

### Step 2: Square both sides
Next, we square both sides to eliminate the square root:
\[ \left(\sqrt{x} - \frac{1}{\sqrt{x}}\right)^2 = (2\sqrt{2})^2 \]
This simplifies to:
\[ \left(\sqrt{x}\right)^2 - 2\left(\sqrt{x}\right)\left(\frac{1}{\sqrt{x}}\right) + \left(\frac{1}{\sqrt{x}}\right)^2 = 8 \]
Which can be rewritten as:
\[ x - 2 + \frac{1}{x} = 8 \]

### Step 3: Rearrange the equation
Now, we rearrange the equation:
\[ x + \frac{1}{x} - 2 = 8 \]
Adding 2 to both sides gives:
\[ x + \frac{1}{x} = 10 \]

### Step 4: Square again
Next, we square both sides again to find \( x^2 + \frac{1}{x^2} \):
\[ \left(x + \frac{1}{x}\right)^2 = 10^2 \]
This expands to:
\[ x^2 + 2 + \frac{1}{x^2} = 100 \]

### Step 5: Solve for \( x^2 + \frac{1}{x^2} \)
Now we can isolate \( x^2 + \frac{1}{x^2} \):
\[ x^2 + \frac{1}{x^2} = 100 - 2 \]
Thus, we find:
\[ x^2 + \frac{1}{x^2} = 98 \]

### Final Answer
The value of \( x^2 + \frac{1}{x^2} \) is \( \boxed{98} \).