Evaluate: \(\sqrt{12 + \sqrt{12 + \sqrt{12 + \cdots}}}\)
4
Let \(x = \sqrt{12 + \sqrt{12 + \sqrt{12+\cdots}}}\). Then \(x = \sqrt{12+x}\)
\(x^2 = 12 + x \Rightarrow x^2 - x - 12 = 0\)
\((x-4)(x+3) = 0\)
Since x must be positive, \(x = \mathbf{4}\)
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