Question

if p=2-√3 then find the value of p²-1/p²​

Answer 1

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Answer 2

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If p=2-√3 then , find the value of p²-1/p².

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$\tt \frac{(2 - \sqrt{3})^2}{1} - \frac{1}{(2 - \sqrt{3})^2} \\ \tt \implies \frac{4 + 3 - 4\sqrt{3}}{1} - \frac {1}{4 + 3 - 4\sqrt{3}} \\ \tt \implies \frac {7 - 4\sqrt{3}}{1} - \frac {1}{7 - 4\sqrt{3}} \\ \tt \implies \frac {(7 - 4\sqrt{3})^2 - 1}{7 - 4\sqrt{3}} \\ \tt \implies \frac {49 + 48 - 56\sqrt{3} - 1}{7 - 4\sqrt{3}} \times \frac {7 + 4\sqrt{3}}{7 + 4\sqrt{3}} \\ \tt \implies \frac {(96 - 56\sqrt{3})(7 + 4\sqrt{3})}{49 - 48} \\ \tt \implies \frac {672 - 392\sqrt {3} + 384\sqrt {3} - 672}{1} \\ \tt \implies - 8\sqrt {3}$

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