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

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

A.

9

B.

18

C.

24

D.

27

View answer & explanation

Correct answer is C

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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