Question

If x = 2-√3 then x2 - 1/x2 is ​

Answer 1

Answer:

$x = 2 - \sqrt{3}$

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

${x}^{2} = 4 + 3 - 4 \sqrt{3}$

${x}^{2} = 7 - 4 \sqrt{3}$

$\frac{1}{ {x}^{2} } = \frac{1}{7 - 4 \sqrt{3} } \times \frac{7 + 4 \sqrt{3} }{7 + 4 \sqrt{3} }$

$\frac{1}{ {x}^{2} } = \frac{7 + 4\sqrt{3} }{49 - 48}$

$\frac{1}{ {x}^{2} } = 7 + 4 \sqrt{3}$

${x}^{2} - \frac{1}{ {x}^{2} } = 7 - 4 \sqrt{3} - 7 - 4 \sqrt{3}$

${x}^{2} - \frac{1}{ {x}^{2} } = - 8 \sqrt{3}$

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