Question

pps solve this,a=2+√3,find a-1/a

Answer 1

$\large \tt AHOY!! \:$

$\rm given \: the \: value \: of \: a = 2 + \sqrt{3} \\ \\ \therefore \rm \frac{1}{a} = \frac{1}{2 + \sqrt{3} } \\ \\ \rm = \frac{1}{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } \\ \\ = \rm \frac{2 - \sqrt{3} }{(2 + \sqrt{3})(2 - \sqrt{3} ) } \\ \\ = \rm \frac{2 - \sqrt{3} }{( {2})^{2} - ( { \sqrt{3}) }^{2} } \\ \\ = \rm \frac{2 - \sqrt{3} }{4 - 3} \\ \\ \rm = 2 - \sqrt{3} \\ \\ \rm \therefore a - \frac{1}{a} =( 2 + \sqrt{3} ) - (2 - \sqrt{3} ) \\ \\ \rm = \cancel2 + \sqrt{3} - \cancel2 + \sqrt{3} \\ \\ \rm = 2 \sqrt{3}$


$\large \tt HOPE \: THIS \: HELPS!!$