Discussion

Question:

Let x = $\sqrt{4 + \sqrt{4 - \sqrt{4 + \sqrt{4 - . . . . t o i n f i n i t y .}}}}$ Then x equals

Explanation:

x = $\sqrt{4 + \sqrt{4 - \sqrt{4 + \sqrt{4 - . . . . t o i n f i n i t y}}}}$

∴ x² - 4 = $\sqrt{4 - \sqrt{4 + \sqrt{4 - . . . . t o i n f i n i t y}}}$

∴ (x² - 4)² - 4 = - $\sqrt{4 + \sqrt{4 - . . . t o i n f i n i t y}}$

∴ (x² - 4)² - 4 = - x

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

Hence, option (c).

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