If `x^2+1/x^2=34`, then find the value of `x+1/x`

Options

A. 4
B. 6
C. 8
D. 17

Answer

To solve the equation \( x^2 + \frac{1}{x^2} = 34 \) and find the value of \( x + \frac{1}{x} \), we can follow these steps:

### Step 1: Use the identity
We know that:
\[ x^2 + \frac{1}{x^2} = \left( x + \frac{1}{x} \right)^2 - 2 \]
Let \( y = x + \frac{1}{x} \). Then we can rewrite the equation as:
\[ x^2 + \frac{1}{x^2} = y^2 - 2 \]

### Step 2: Substitute the given value
Substituting the given value into the equation:
\[ y^2 - 2 = 34 \]

### Step 3: Solve for \( y^2 \)
Add 2 to both sides:
\[ y^2 = 34 + 2 \]
\[ y^2 = 36 \]

### Step 4: Take the square root
Now, take the square root of both sides:
\[ y = \sqrt{36} \]
\[ y = 6 \quad \text{(since \( x + \frac{1}{x} \) is positive)} \]

### Conclusion
Thus, the value of \( x + \frac{1}{x} \) is:
\[ \boxed{6} \]