To solve the problem (assuming the question is: If (x + \frac{1}{x} = 3), find (x^2 + \frac{1}{x^2})), follow these steps:

Step 1: Square both sides of the given equation

We know:
[x + \frac{1}{x} = 3]

Square both sides:
[ \left(x + \frac{1}{x}\right)^2 = 3^2 ]

Step 2: Expand the left-hand side

Using the identity ((a + b)^2 = a^2 + 2ab + b^2):
[x^2 + 2 \cdot x \cdot \frac{1}{x} + \frac{1}{x^2} = 9]

Simplify the middle term ((2 \cdot x \cdot \frac{1}{x} = 2)):
[x^2 + 2 + \frac{1}{x^2} = 9]

Step 3: Solve for (x^2 + \frac{1}{x^2})

Subtract 2 from both sides:
[x^2 + \frac{1}{x^2} = 9 - 2 = 7]

Answer: (\boxed{7})

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