Question

if x=3-2√2, then value of x+1/x is​

Answer 1

Step-by-step explanation:

Answer in the attachment

Answer 2

$\\ \\ \large\underline{ \underline{ \sf{ \red{given:} }}}$

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

$\\ \\ \large\underline{ \underline{ \sf{ \red{to \: find:} }}} \\ \\ \sf \: x + \frac{1}{x} \\ \\ \large\underline{ \underline{ \sf{ \red{solution:} }}}$

$\sf \: x = 3 - 2 \sqrt{2} \\ \\ \\ \sf \: taking \: reciprocal \: we \: get \\ \\ \\ \sf \: \frac{1}{x} = \frac{1}{3 - 2 \sqrt{2} } \\ \\ \\ \sf \: rationalising \: factor \: is \: (3 + 2 \sqrt{2} ) \\ \\ \\ \sf \: \frac{1}{x} = \frac{1}{3 - 2 \sqrt{2} } \times \frac{3 + 2 \sqrt{2} }{3 + 2 \sqrt{2} } \\ \\ \\ \sf \: \frac{1}{x} = \frac{3 + 2 \sqrt{2} }{(3 - 2 \sqrt{2} )(3 + 2 \sqrt{2}) } \\ \\ \\ \sf \: \frac{1}{x} = \frac{3 + 2 \sqrt{2} }{ {3}^{2} - ( {2 \sqrt{2}) }^{2} } \\ \\ \\ \sf \: \frac{1}{x} = \frac{3 + 2 \sqrt{2} }{9 - 8} \\ \\ \\ \sf \: \blue{\frac{1}{x} = 3 + 2 \sqrt{2} }$

Also ,

$\\ \sf \: \blue{x = 3 - 2 \sqrt{2} } \\ \\ \\ \sf \: adding \: both \: we \: get \\ \\ \\ \sf \: x + \frac{1}{x} = 3 - \cancel{2 \sqrt{2} } + 3 + \cancel{ 2 \sqrt{2} } \\ \\ \\ \therefore \sf \: \boxed{ \sf \: \orange{x + \frac{1}{x} = 6 }}$