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(A) Let the sum be $S = x + \frac{1}{x}$.By the Arithmetic Mean-Geometric Mean $(AM-GM)$ inequality,for positive real numbers $x$ and $\frac{1}{x}$:$\

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(A) Let the sum be $S = x + \frac{1}{x}$.By the Arithmetic Mean-Geometric Mean $(AM-GM)$ inequality,for positive real numbers $x$ and $\frac{1}{x}$:$\frac{x + \frac{1}{x}}{2} \ge \sqrt{x \cdot \frac{1}{x}}$$\frac{x + \frac{1}{x}}{2} \ge \sqrt{1}$$x + \frac{1}{x} \ge 2$.The minimum value of the sum is $2$,which occurs when $x = \frac{1}{x}$,i.e.,$x^2 = 1$. Since $x$ is a positive real number,$x = 1$.

For a positive real number $x$,when its reciprocal is added to it,the sum attains a minimum value. What is the value of $x$?

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