Question

If
$x = (2 + \sqrt{3})$
find the value of
$x {}^{2} + \frac{1}{x {}^{2} }$
​

Answer 1

1/x = 1/(2+√3)

= 4-3)/(2+√3)

= (2-√3)( √3+ 2)/(2+√3)

= 2-√3

x^2 + 1/x^2

( x+ 1/x)^2 - 2

( 2+ √3 + 2-√3)^2 -2

(4)^2 -2

16-2

14