Question

Find x2-1/x2 when x=5-2under root 6

Answer 1

hey your answer is in this image hope it helps u

Answer 2

$x = 5 - 2 \sqrt{6} \\ \\ \frac{1}{x} = \frac{1}{5 - 2 \sqrt{6} } \\ \\ \frac{1}{x} = \frac{1}{5 - 2 \sqrt{6} } \times \frac{5 + 2 \sqrt{6} }{5 + 2 \sqrt{6} } \\ \\ \frac{1}{x} = \frac{5 + 2 \sqrt{6} }{25 - 24} \\ \\ \frac{1}{x} = 5 + 2 \sqrt{6}$

Now,

${x}^{2} - \frac{1}{ {x}^{2} } = {(5 - 2 \sqrt{6} )}^{2} - {(5 + 2 \sqrt{6} )}^{2} \\ \\ = (25 + 24 - 20 \sqrt{6} ) - (25 + 24 + 20 \sqrt{6} ) \\ \\ = 49 - 20 \sqrt{6} - 49 - 20 \sqrt{6} \\ \\ = - 40 \sqrt{6}$