If `(a + (1)/(a))^(2)` = 3 then the value of `(a^(2) + (1)/( a^(2)))` will be

Options

A. 0
B. 1
C. 2
D. 3

Answer

To solve the problem, we start with the equation given:

\[ (a + \frac{1}{a})^2 = 3 \]

### Step 1: Expand the left-hand side
Using the formula for the square of a binomial, we can expand the left-hand side:

\[ (a + \frac{1}{a})^2 = a^2 + 2 \cdot a \cdot \frac{1}{a} + \frac{1}{a^2} \]

This simplifies to:

\[ a^2 + 2 + \frac{1}{a^2} \]

### Step 2: Set the expanded equation equal to 3
Now, we can set the expanded equation equal to 3:

\[ a^2 + 2 + \frac{1}{a^2} = 3 \]

### Step 3: Isolate \(a^2 + \frac{1}{a^2}\)
To isolate \(a^2 + \frac{1}{a^2}\), we subtract 2 from both sides:

\[ a^2 + \frac{1}{a^2} = 3 - 2 \]

This simplifies to:

\[ a^2 + \frac{1}{a^2} = 1 \]

### Final Answer
Thus, the value of \(a^2 + \frac{1}{a^2}\) is:

\[ \boxed{1} \]

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