Question

Plz solve this question

Answer 1

since
p=2-√3,
then
1/p =2+√3,

hence
p²-1/p² =(2-√3)² - (2+√3)²,

p² - 1/p² = (4+3-4√3) - (4+3+4√3),

=7-4√3-7-4√3,

=-8√3

Answer 2

p = 2-$\sqrt{3}$

so, $\frac{1}{p}  = \frac{1}{2-\sqrt{3}}$  

or,  $\frac{1}{2-\sqrt{3}} *  \frac{2+\sqrt{3}}{2+\sqrt{3}}   = \frac{2+\sqrt{3}}{2^{2}   -(\sqrt{3})^2 }  =\frac{2+\sqrt{3}}{1}   = 2+\sqrt{3}$

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

or, $(4 + 3 - 4\sqrt{3}) - 4 - 3 - 4\sqrt{3}  =  -8\sqrt{3}$

∴Thus, the answer is $-8\sqrt{3}$