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Explanation:

x = $\sqrt{4+\sqrt{4-\sqrt{4+\sqrt{4-....to infinity}}}}$

∴ x² - 4 = $\sqrt{4-\sqrt{4+\sqrt{4-.... to infinity}}}$

∴ (x² - 4)² - 4 = - $\sqrt{4+\sqrt{4-...to infinity}}$

∴ (x² - 4)² - 4 = - x

Now, substituting options, we find that only option (c) satisfies the above equation.

Hence, option (c).