If `P- 1/P = 6 ` , then the value of `P^2 + 1/P^2` will be -

Options

A. 48
B. 36
C. 37
D. 40

Answer

To solve the equation \( P - \frac{1}{P} = 6 \) and find the value of \( P^2 + \frac{1}{P^2} \), we can follow these steps:

### Step 1: Start with the given equation
We have:
\[ P - \frac{1}{P} = 6 \]

### Step 2: Square both sides
To eliminate the fraction, we square both sides of the equation:
\[ \left(P - \frac{1}{P}\right)^2 = 6^2 \]
This simplifies to:
\[ P^2 - 2P\cdot\frac{1}{P} + \left(\frac{1}{P}\right)^2 = 36 \]

### Step 3: Simplify the squared equation
The term \( -2P\cdot\frac{1}{P} \) simplifies to \( -2 \):
\[ P^2 - 2 + \frac{1}{P^2} = 36 \]

### Step 4: Rearrange the equation
Now, we can rearrange the equation to isolate \( P^2 + \frac{1}{P^2} \):
\[ P^2 + \frac{1}{P^2} = 36 + 2 \]

### Step 5: Calculate the final value
Now, we can calculate:
\[ P^2 + \frac{1}{P^2} = 38 \]

Thus, the value of \( P^2 + \frac{1}{P^2} \) is \( 38 \).

### Final Answer
The value of \( P^2 + \frac{1}{P^2} \) is \( 38 \).

---