<p>The real positive number <span style='font-style:italic'>x</span> when added to its inverse gives the minimum value of the sum at <span style='font-style:italic'>x</span> equal to</p>
Step-by-Step Solution
Key Concept: Apply AM-GM inequality to find the minimum value of x + 1/x for positive x.
<p>For a positive real number <span style='font-style:italic'>x</span>, we need to minimize <span style='font-style:italic'>f(x) = x + 1/x</span>.</p><p>By AM-GM inequality: <span style='font-style:italic'>x + 1/x</span> ≥ 2√(<span style='font-style:italic'>x</span> · <span style='font-style:italic'>1/x</span>) = 2.</p><p>Equality holds when <span style='font-style:italic'>x = 1/x</span>, which gives <span style='font-style:italic'>x</span> = 1.</p><p>∴ The answer is (C) 1.</p>
Correct Answer: C