Question

If x=2+√3 then x+1/x=?​

Answer 1

Solution;

Given:-

$\rm x=2+\sqrt{3}$

To find

$\implies\rm x+\dfrac{1}{x}$

now put the value of x on given equation

$\implies2+\sqrt{3} +\dfrac{1}{2+\sqrt{3} }$

Taking LCM

$\implies\dfrac{(2+\sqrt{3})(2+\sqrt{3})+1 }{(2+\sqrt{3})}$

Using this identities; ( a + b )² = a² + b² + 2ab

$\implies\dfrac{2^{2}+(\sqrt{3})^{2} +2\times2\times\sqrt{3}+1 }{2+\sqrt{3} }$

$\implies\dfrac{4+3+4\sqrt{3} +1}{2+\sqrt{3} }$

$\implies\dfrac{8+4\sqrt{3} }{2+\sqrt{3} }$

$\implies\dfrac{4(2+\sqrt{3}) }{2+\sqrt{3} } =4$

Answer= 4