Question

plz slv thus question

Answer 1

Given x = 3 - 2root 2.

Then x^2 = (3 - 2 root 2)^2

                = (3)^2 + (2 root 2)^2 - 2 * 3 * 2 root 2

                = 9 + 8 - 12root 2.

               = 17 - 12root 2.


Now,..

1/x^2 = 1/17 - 12 root 2

On rationalizing, we get

$\frac{1}{17 - 12 \sqrt{2} } * \frac{17 + 12 \sqrt{2} }{17 + 12 \sqrt{2} }$

$\frac{17 + 12 \sqrt{2} }{(17 + 12 \sqrt{2}(17 - 12 \sqrt{2}) }$

$\frac{17 + 12 \sqrt{2} }{289 - 288}$

$17 + 12 \sqrt{2}$


Now,

$x^2 - \frac{1}{x^2} = 17 - 12 \sqrt{2} - 17 - 12 \sqrt{2}$

                                   $= -24 \sqrt{2}$


Hope this helps!