Correct Answer: Option C

Explanation

x = 3 - \(\sqrt{3}\)

x² = (3 - \(\sqrt{3}\))²

= 9 + 3 - 6\(\sqrt{34}\)

= 12 - 6\(\sqrt{3}\)

= 6(2 - \(\sqrt{3}\))

∴ x² + \(\frac{36}{x^2}\) = 6(2 - \(\sqrt{3}\)) + \(\frac{36}{6(2 - \sqrt{3})}\)

6(2 - \(\sqrt{3}\)) + \(\frac{6}{2 - \sqrt{3}}\) = 6(- \(\sqrt{3}\)) + \(\frac{6(2 + \sqrt{3})}{(2 - \sqrt{3})(2 + \sqrt{3})}\)

= 6(2 - \(\sqrt{3}\)) + \(\frac{6(2 + \sqrt{3})}{4 - 3}\)

6(2 - \(\sqrt{3}\)) + 6(2 + \(\sqrt{3}\)) = 12 + 12

= 24

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