Question

If x=7 + 4√3,
then x + 1/x = ?​

Answer 1

Answer:

The answer is 14

Step-by-step explanation:

Given $x=7+4\sqrt 3$

$\Rightarrow \dfrac{1}{x}=\dfrac{1}{7+4\sqrt 3}\times \dfrac{7-4\sqrt 3}{7-4\sqrt 3}$    Rationalize

         $=\dfrac{7-4\sqrt 3}{7^2-(4\sqrt 3)^2}\\=\dfrac{7-4\sqrt 3}{49-16(3)}\\=\dfrac{7-4\sqrt 3}{49-48}=7-4\sqrt 3$

Therefore $x+\dfrac{1}{x}=7+4\sqrt 3+7-4\sqrt 3=14$