If x=5+2 √(6), then √(x)-1/(√(x)) is · ABC26GN1956
Subject: General Aptitude · Chapter: Surds and Indices · Exam: A.A.O. Exam 2009
If $x=5+2 \sqrt{6}$, then $\sqrt{x}-\frac{1}{\sqrt{x}}$ is
(a)$2 \sqrt{2}$
(b)$2 \sqrt{3}$
(c)$\sqrt{3}+\sqrt{2}$
(d)$\sqrt{3}-\sqrt{2}$
Answer
Explanation
$\left(\sqrt{x}-\frac{1}{\sqrt{x}}\right)^{2}=x+\frac{1}{x}-2=(5+2 \sqrt{6})+\frac{1}{(5+2 \sqrt{6})}-2$ $$\begin{aligned} & =(5+2 \sqrt{6})+\frac{1}{(5+2 \sqrt{6})} \times \frac{(5-2 \sqrt{6})}{(5-2 \sqrt{6})}-2 \\ & =(5+2 \sqrt{6})+(5-2 \sqrt{6})-2=8 \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.
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