If ` (p^(2) + (1)/( p^(2))) = 47` the value of `(p + (1)/(p))` is

Options

A. 5
B. 6
C. 7
D. 8

Answer

To solve the equation \( p^2 + \frac{1}{p^2} = 47 \) and find the value of \( p + \frac{1}{p} \), we can follow these steps:

### Step 1: Rewrite the equation
We start with the equation:
\[ p^2 + \frac{1}{p^2} = 47 \]

### Step 2: Add 2 to both sides
To manipulate the left side into a perfect square, we add 2 to both sides:
\[ p^2 + \frac{1}{p^2} + 2 = 47 + 2 \]
This simplifies to:
\[ p^2 + \frac{1}{p^2} + 2 = 49 \]

### Step 3: Recognize the perfect square
The left side can be factored as a perfect square:
\[ (p + \frac{1}{p})^2 = 49 \]

### Step 4: Take the square root of both sides
Now, we take the square root of both sides:
\[ p + \frac{1}{p} = \sqrt{49} \]
This simplifies to:
\[ p + \frac{1}{p} = 7 \]

### Conclusion
Thus, the value of \( p + \frac{1}{p} \) is:
\[ \boxed{7} \]

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