If x = 3 - √3 3 , find x2 + 36x2

Question 1 Report

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

9

18

24

27

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

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