MathematicsIf x=12−3, then x−1×2=

If $x = \frac{1}{2 - \sqrt{3}}$ , then ${(x - \frac{1}{x})}^{2} =$

A
12
B
4
C
9
D
16

Solution:

$x = 2 + \sqrt{3}, \frac{1}{x} = \frac{1}{2 + \sqrt{3}} = 2 - \sqrt{3}$

$x - \frac{1}{x} = 2 + \sqrt{3} - 2 + \sqrt{3} = 2 \sqrt{3}$

${(x - \frac{1}{x})}^{2} = {(2 \sqrt{3})}^{2} = 12$

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