To solve the problem (assuming the classic question: Given (a + b = 7) and (ab = 12), find (a^2 + b^2)):

Step 1: Use the algebraic identity

We know that:
[a^2 + b^2 = (a + b)^2 - 2ab]

Step 2: Substitute the given values

Given (a + b = 7) and (ab = 12):
[a^2 + b^2 = 7^2 - 2(12)]
[= 49 - 24]
[= 25]

Answer: (\boxed{25})

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