Question

solve this and also suggest me how to solve it please exam if you show in your notebook I surely made ur answer is brainlest

Answer 1

$Given: x = 3 - 2 \sqrt{2}$

$\frac{1}{x} = \frac{1}{3 - 2 \sqrt{2} } * \frac{3 + 2 \sqrt{2} }{3 + 2 \sqrt{2} }$

                        $\frac{3 + 2 \sqrt{2} }{(3 - 2 \sqrt{2})(3 + 2 \sqrt{2)} }$

                        $\frac{3 + 2 \sqrt{2} }{9 - 8}$

                        $\frac{3 + 2 \sqrt{2} }{1}$

                       $3 + 2 \sqrt{2}$



Now,

$x^3 - \frac{1}{x^3} = (x - \frac{1}{3} )^3 + 3 * x * \frac{1}{x}(x - \frac{1}{x})$

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

                                    $= (-4 \sqrt{2} )^3 + 3(-4 \sqrt{2})$

                                    $= -128 \sqrt{2} - 12 \sqrt{2}$

                                   $-140 \sqrt{2}$



Hope this helps!

Answer 2

Hi,

Please see the attached file!


Thanks