Question

find p^2-1/p^2 if p = 2-√3

Answer 1

hope this is helpful

Answer 2

Given :
p=2-√3

To find:
${p}^{2} - \frac{1}{ {p}^{2}} \\ \\ solution \\ \\ p = 2 - \sqrt{3} \\ \\ \frac{1}{p} = \frac{1}{2 - \sqrt{3} } \\ \\ rationalising \: the \: denominator \\ \\ \frac{1}{p} = \frac{1}{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} } \\ \\ \frac{1}{p} = \frac{2 + \sqrt{3} }{ {2}^{2} - { \sqrt{3} }^{2} } \\ \\ \frac{1}{p} = \frac{2 + \sqrt{3} }{4 - 3} \\ \\ \frac{1}{p} = \frac{2 + \sqrt{3} }{1} \\ \\ \frac{1}{p} = 2 + \sqrt{3} \\ \\ = {p}^{2} - \frac{1}{ {p}^{2} } \\ \\ = {(2 - \sqrt{3}) }^{2} - {(2 + \sqrt{3}) }^{2} \\ \\ = {(2)}^{2} + {( \sqrt{3} )}^{2} - 2 \times 2 \times \sqrt{3} - ( {(2)}^{2} + {( \sqrt{3} )}^{2} + 2 \times 2 \times \sqrt{3} ) \\ \\ = 4 + 3 - 4 \sqrt{3} - (4 + 3 + 4 \sqrt{3} ) \\ \\ = 7 - 4 \sqrt{3} - 7 - 4 \sqrt{3} \\ \\ = - 8 \sqrt{3}$