If x = 3 – (sqrt{3}), find x2 + (frac{36}{x^2})

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