It seems the original problem details (image content) are missing, but based on common algebraic problems, let’s assume a typical scenario:

Assumed Problem:

If (a + \frac{1}{a} = 3), find (a^2 + \frac{1}{a^2}).

Solution:

Using the identity ((x + y)^2 = x^2 + 2xy + y^2):
Square both sides of (a + \frac{1}{a} = 3):
[ \left(a + \frac{1}{a}\right)^2 = 3^2 ]
[ a^2 + 2 \cdot a \cdot \frac{1}{a} + \frac{1}{a^2} = 9 ]
[ a^2 + 2 + \frac{1}{a^2} = 9 ]

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

Answer: (\boxed{7})

(Note: If the problem was different, adjust based on actual details, but this is a common result.)

(\boxed{7})

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