If x = 3 - √3 3 , find x2 + 36x2

If x = 3 - $\sqrt{3}$, find x2 + $\frac{36}{x^2}$

Answer Details

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