If x = 3 - \(\sqrt{3}\), find x
2 + \(\frac{36}{x^2}\)
A. 9
B. 18
C. 24
D. 27
Correct Answer: 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
