Question

if X = (2) + underoot (3 )find the
value of( x )square + (1 )upon (X) square answer /SOLVE IT PLEASE/

Answer 1

x=2√3
x^2+1/x^2=
[2√3]^2+1/(2√3)^2
(2^2+{√3^2}+2×2√3)+(1/2^2+{√3}^2+2×2√3
(4+3+4√3)+1/4+3+4√3
On rationalising
7+4√3+[1/【7+4√3】]×7-4√3/6-4√3
7+4√3+7-4√3/(7)^2-(4)^2(√3)^2
7+4√3+7-4√3/49-(16×3)
7+4√3+7-4√3/49-48
7+4√3+7-4√3/1
On cancellation
7+7
=14

Answer 2

Hello Mate!

$x = 2 + \sqrt{3} \\ \frac{1}{x} = \frac{1}{2 + \sqrt{3} } = \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } \\ = \frac{2 - \sqrt{3} }{4 - 3} = 2 - \sqrt{3} \\ {x}^{2} = {(2 + \sqrt{3}) }^{2} \\ = 4 + 3 + 4 \sqrt{3} \\ = 7 + 4 \sqrt{3} \\ \frac{1}{ {x}^{2} } = {(2 - \sqrt{3}) }^{2} \\ 4 + 3 - 4 \sqrt{3} = 7 - 4 \sqrt{3} \\ 7 + 4 \sqrt{3} + 7 - 4 \sqrt{3} = 14$
Hope it helps☺!