Question:
<p>A rod of fixed length 2 slides along the coordinate axes. If it meets the axes at A(a, 0) and B(0, b), then the minimum value of <span class="math-tex">\(\left(a+\frac{1}{a}\right)^{2}+\left(b+\frac{1}{b}\right)^{2}\)</span> equals : </p>
<p style="display:inline">10</p>
<p style="display:inline">7</p>
<p style="display:inline">8</p>
<p style="display:inline">9</p>
Step-by-Step Solution
Key Concept: Use the rod length to establish the constraint $a^2 + b^2 = 4$ and minimize the expanded expression by applying the AM-GM inequality to the $a^2b^2$ term.
<p>9</p>
Correct Answer: D