If the value of `a^(2)+(1)/(a^(2))` is 786, then the value of `a-(1)/(a)` is ___________.

Options

A. `pm23`
B. `pm25`
C. `pm17`
D. `pm28`

Answer

To solve the problem where \( a^2 + \frac{1}{a^2} = 786 \) and we need to find the value of \( a - \frac{1}{a} \), we can follow these steps:

### Step 1: Use the identity for \( a^2 + \frac{1}{a^2} \)
We know that:
\[ a^2 + \frac{1}{a^2} = \left( a - \frac{1}{a} \right)^2 + 2 \]
This means we can rewrite the equation as:
\[ \left( a - \frac{1}{a} \right)^2 + 2 = 786 \]

### Step 2: Rearrange the equation
Subtract 2 from both sides:
\[ \left( a - \frac{1}{a} \right)^2 = 786 - 2 \]
\[ \left( a - \frac{1}{a} \right)^2 = 784 \]

### Step 3: Take the square root of both sides
Now, we take the square root:
\[ a - \frac{1}{a} = \pm \sqrt{784} \]

### Step 4: Calculate the square root
Calculating the square root of 784:
\[ \sqrt{784} = 28 \]
Thus, we have:
\[ a - \frac{1}{a} = \pm 28 \]

### Final Answer
Therefore, the value of \( a - \frac{1}{a} \) is:
\[ \boxed{28} \text{ or } \boxed{-28} \]

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