Question

if
$x =3 - 2 \sqrt{2} find \: x - \frac{1}{x} \: is \: rational \: o \: irrtiona$
Or irrational

Answer 1

Hey mate !

1/x = 1/3-2√2

= 3+2√2/3²-2√2²

= 3+2√2/9-8

= 3+2√2/1

x-1/x => 3-2√2 -(3+2√2)

==> 3-2√2-3-2√2

==> -4√2

$-4\sqrt2\text\: {is a irrational number .}$

Thanks

Answer 2

$\huge \sf{Given :-) }$

$\huge \bf{x = 3 - 2 \sqrt{2} }.$


$\huge \sf{To \: Find :-)}$


$\huge \bf{ = > x - \frac{1}{x} }.$




$\bf \huge= > \frac{1}{x} = \frac{1}{3 - 2 \sqrt{2} } .$



$\huge = \frac{1}{3 - 2 \sqrt{2} } \times \frac{3 + 2 \sqrt{2} }{3 + 2 \sqrt{2} } .$




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




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



$\huge \bf = 3 + 2 \sqrt{2} .$


NOW,


$\huge \bf = x - \frac{1}{x} .$



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



$\bf = 3 - 2 \sqrt{2} - 3 - 2 \sqrt{2}.$



$\bf = \cancel3 - 2 \sqrt{2} - \cancel 3 - 2 \sqrt{2} .$



$\huge \boxed{ = - 4 \sqrt{2} .}$


✔✔Hence, it is irrational number ✅✅.




$\huge \boxed{THANKS}$


$\huge \bf{ \#BeBrainly.}$