If `x+1/(x)=5`, then the value of `x^(2)+1/(x^(2))` is:

Options

A. A)23
B. B)25
C. C)29
D. D)27

Answer

To solve the equation \( x + \frac{1}{x} = 5 \) and find the value of \( x^2 + \frac{1}{x^2} \), we can follow these steps:

### Step 1: Square both sides of the equation
We start with the equation:
\[ x + \frac{1}{x} = 5 \]
Now, we square both sides:
\[ \left( x + \frac{1}{x} \right)^2 = 5^2 \]

### Step 2: Expand the left side
Using the identity \( (a + b)^2 = a^2 + 2ab + b^2 \), we expand the left side:
\[ x^2 + 2 \cdot x \cdot \frac{1}{x} + \frac{1}{x^2} = 25 \]
This simplifies to:
\[ x^2 + 2 + \frac{1}{x^2} = 25 \]

### Step 3: Isolate \( x^2 + \frac{1}{x^2} \)
Now, we need to isolate \( x^2 + \frac{1}{x^2} \):
\[ x^2 + \frac{1}{x^2} + 2 = 25 \]
Subtract 2 from both sides:
\[ x^2 + \frac{1}{x^2} = 25 - 2 \]

### Step 4: Calculate the final value
Now, we perform the subtraction:
\[ x^2 + \frac{1}{x^2} = 23 \]

Thus, the value of \( x^2 + \frac{1}{x^2} \) is \( 23 \).

### Final Answer
\[ \boxed{23} \]