Question

If $x=7+4\sqrt{3}$, then the value of $x^{\frac{1}{2}}+x^{-\frac{1}{2}}$ is?

• A. $4$
• B. $5$
• C. $3$
• D. $6$

Answer 1

The correct option is A $4$

$x=7+4\sqrt{3}x=4+3+4\sqrt{3}x={\left(2\right)}^2+{\left(\sqrt{3}\right)}^2+2.2\sqrt{3}x={\left(2+\sqrt{3}\right)}^2\sqrt{x}+\frac{1}{\sqrt{x}}\Rightarrow 2+\sqrt{3}+\frac{1}{2+\sqrt{3}}\Rightarrow 2+\sqrt{3}+\frac{2-\sqrt{3}}{4-3}\Rightarrow 2=\sqrt{3}+2-\sqrt{3}\Rightarrow 4Ans.$