Question

x
= 3-2√2
find
the value of
x² - 1/x^2​

Answer 1

Answer:

$x = 3 - 2 \sqrt{2} \\ \frac{1}{x} = \frac{1}{3 - 2 \sqrt{2}} \times \frac{3 + 2 \sqrt{2}}{3 + 2 \sqrt{2}} \\ \: \: \: = \frac{3 + 2 \sqrt{2}}{( {3})^{2} -(2 \sqrt{2} ) ^{2} } \\ \: \: \: = \frac{3 + 2 \sqrt{2}}{9 - 8} \\ \: \: \: = 3 + 2 \sqrt{2} \\ x + \frac{1}{x} \\ = 3 - 2 \sqrt{2} + 3 + 2 \sqrt{2} \\ = 6 \: \: \: \: \: \: \: \: \: \: ....(1) \\x - \frac{1}{x} \\ = 3 - 2 \sqrt{2} - 3 - 2 \sqrt{2} \\ = - 4 \sqrt{2} \: \: \: \: \: ....(2)\\ now \\ {x}^{2} - \frac{1}{ {x}^{2} } =( x + \frac{1}{x})(x - \frac{1}{x} ) \\ = 6 \times ( - 4 \sqrt{2}) \: \: \: \: \: \: \: \: \: \: \: (from \: 1 \: and \: 2)\\ = - 24 \sqrt{2}$