Question

If x=2-root3 then find tha value of x+1/x​

Answer 1

$\huge \underline{ \overline{ \mid{ \bold{ \blue{answer}} \mid}}} \\ \sf \: x = 2 \sqrt{3} \\ \sf \: \frac{1}{x} = \frac{(2 - \sqrt{3)} }{(2 + \sqrt{3)} (2 - \sqrt{3)} } ( rationalising \: denominator) \\ \sf \: \frac{1}{x} = \frac{( 2 - \sqrt{3}) }{ ({2}^{2} - \sqrt{3} {})^{2} } \\ \sf \: \frac{1}{x} = \frac{(2 - \sqrt{3}) }{(4 - 3)} \\ \sf \frac{1}{x} = 2 - \sqrt{3} \\ \sf \: thus \: x + \frac{1}{x} = 2 + \sqrt{3} + 2 - \sqrt{3} \\ \sf = > x + \frac{1}{x} = 4 \\ \bf \: = > (x + \frac{1}{x} ) {}^{2} = 16$