Question

$if \\ \:x = 2 + \sqrt{3}$
$fi nd \\ {x }^{2} + \frac{1}{x {}^{2} }$

Answer 1

Hi,

Here's the solution :-

x = 2 + root 3

=>x^2 =[ 2 + root 3 ] ^2

=> x^2 = 5 + 4 root 3

=> x^2 + 1/x^2 = 5 + 4 root 3 + 1/(5 + 4 root 3)

Hope it helps ^_^

Answer 2

Hey friend

Here is your answer

x=2+√3

1/x=1/(2+√3)

1/x=(2-√3)/[(2+√3)(2-√3)]

1/x=(2-√3)/(2²-(√3)²)

1/x=(2-√3)/(4-3)

1/x=2-√3

Value of x²+(1/x²)

=x²+(1/x²)

=(2+√3)²+(2-√3)²

=4+3+2√3+4+3-2√3

=7+7

=14

HOPE THIS HELPS YOU