Question

if x=2+√3 then find the value of x+1÷x

Answer 1

x = 2 + √3

1/x  =         1        =         2 - √3          =  2 - √3

            2 + √3            (2)²  - (√3)²

x + 1/x  = 2 + √3  + 2 - √3 =  4

Answer 2

Here is your answer

$(2 + \sqrt{3} ) + 1 \div (2 + \sqrt{3} ) \\ = (2 + \sqrt{3} ) + (2 - \sqrt{3} ) \div (2 {}^{2} - \sqrt{3} {}^{2} ) \\ = (2 + \sqrt{3} ) + (2 - \sqrt{3} ) \div 1 \\ = 2 + \sqrt{3} + 2 - \sqrt{3} \\ = 4$
Hope it helps you