If `x+1//x=3` , then `3(x^(2)+1//x^(2))` is equal to

Answer

To solve the equation \( x + \frac{1}{x} = 3 \) and find the value of \( 3\left(x^2 + \frac{1}{x^2}\right) \), we can follow these steps:

### Step 1: Square both sides of the equation
We start with the equation:
\[ x + \frac{1}{x} = 3 \]
Now, we square both sides:
\[ \left(x + \frac{1}{x}\right)^2 = 3^2 \]
This gives us:
\[ x^2 + 2\cdot x \cdot \frac{1}{x} + \frac{1}{x^2} = 9 \]

### Step 2: Simplify the equation
The term \( 2 \cdot x \cdot \frac{1}{x} \) simplifies to \( 2 \):
\[ x^2 + 2 + \frac{1}{x^2} = 9 \]

### Step 3: Rearrange the equation
Now, we can rearrange the equation to isolate \( x^2 + \frac{1}{x^2} \):
\[ x^2 + \frac{1}{x^2} = 9 - 2 \]
\[ x^2 + \frac{1}{x^2} = 7 \]

### Step 4: Multiply by 3
Now that we have \( x^2 + \frac{1}{x^2} \), we can find \( 3\left(x^2 + \frac{1}{x^2}\right) \):
\[ 3\left(x^2 + \frac{1}{x^2}\right) = 3 \cdot 7 = 21 \]

### Final Answer
Thus, the value of \( 3\left(x^2 + \frac{1}{x^2}\right) \) is:
\[ \boxed{21} \]

---