If x = 7 - 4 3 , then x + 1 x is equal to?

Answer: Option D

$$\begin{array}{rl}& x=7-4\sqrt{3}\\ & \Rightarrow x=4+3-4\sqrt{3}\\ & \Rightarrow x={\left(2\right)}^2+{\left(\sqrt{3}\right)}^2-2\times 2\sqrt{3}\\ & \Rightarrow {\left(2-\sqrt{3}\right)}^2\\ & \therefore \left[a^2+b^2-2ab={\left(a-b\right)}^2\right]\\ & \Rightarrow x={\left(2-\sqrt{3}\right)}^2\\ & \Rightarrow \sqrt{x}=2-\sqrt{3}\\ & \Rightarrow \frac{1}{\sqrt{x}}=\frac{1}{2-\sqrt{3}}\times \frac{2+\sqrt{3}}{2+\sqrt{3}}\\ & \Rightarrow 2+\sqrt{3}\\ & \therefore \sqrt{x}\text{ + }\frac{1}{\sqrt{x}}\\ & =2-\sqrt{3}+2+\sqrt{3}\\ & =4\end{array}$$