If x=3+2 √(2), find the value of (√(x)-1/(√(x))). · ABC26GN1887
Subject: General Aptitude · Chapter: Surds and Indices
If $x=3+2 \sqrt{2}$, find the value of $\left(\sqrt{x}-\frac{1}{\sqrt{x}}\right)$.
Answer
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Explanation
$\left(\sqrt{x}-\frac{1}{\sqrt{x}}\right)^{2}=x+\frac{1}{x}-2=(3+2 \sqrt{2})+\frac{1}{(3+2 \sqrt{2})}-2=(3+2 \sqrt{2})+\frac{1}{(3+2 \sqrt{2})} \times \frac{(3-2 \sqrt{2})}{(3-2 \sqrt{2})}-2=(3+2 \sqrt{2})+(3-2 \sqrt{2})-2=4. \therefore\left(\sqrt{x}-\frac{1}{\sqrt{x}}\right)=2.$
Explanation as extracted from the printed page; notation may be imperfect.
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