Question

if
$x = 2 + \sqrt{3}$
find
$x - \frac{1}{x}$
and
${x}^{2} + \frac{1}{ {x}^{2} }$
​

Answer 1

Step-by-step explanation:

1)

$(2 + \sqrt{3)} - \frac{1}{2 + \sqrt{3} }$

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

$\frac{2 - \sqrt{3} }{4 - 3}$

=

$2 + \sqrt{3} - 2 - \sqrt{3}$

=0

2.

$( {2 + \sqrt{3)} }^{2} - \frac{1}{( {2 + \sqrt{3)} }^{2} }$

${(4 + 3)}^{2} - \frac{1}{ {(4 + 3)}^{2} }$

Put identity (a+b)² = a²+2ab+b²