Question

if x =(2+root3) find the value of x²+1/x²

Answer 1

If x= 2+sqrt3
Then,
1/x=2-sqrt3 (by rationaliztion denominator)

Then                       (x+1/x)^2 = x^2+(1/x)^2 +2*x*(1/x)
That is (2+sqrt3 +2-sqrt3)^2=x^2 +(1/x)^2+2
                                     4^2 -2=x^2+(1/x)^2
Therefore, 14 is the answer

Answer 2

hey!
#Ur Ans
____________

Given that
X = 2+√3
then

1/X = 1/2+√3

==> 1/2+√3 × (2-√3)/(2-√3)

==> 2-√3/4-3

1/X = 2-√3

now

$(x + \frac{1}{x}) {}^{2} = x {}^{2} + \frac{1}{ {x}^{2} } + 2 \\ \\ = > (2 + \sqrt{3 } + 2 - \sqrt{3} {)}^{2} = {x}^{2} + \frac{1}{ {x}^{2} } + 2 \\ \\ = > (4 {)}^{2} = {x}^{2} + \frac{1}{ {x}^{2} } + 2 \\ \\ = > 16 = {x }^{2} + \frac{1}{ {x}^{2} } + 2 \\ \\ = > {x}^{2} + \frac{1}{ {x}^{2} } = 14 \: ans$
✌☺