Basic Mathematics & Logarithm
Inequalities
Grade 11
Question:
<p>If <span style='font-style:italic'>a, b, c</span> are three positive real numbers, then <span style='font-style:italic'>\(\frac{a}{b}+\frac{b}{c}+\frac{c}{a}\)</span> can never be equal to</p>
<p>(A) 1</p>
<p>(B) 2</p>
<p>(C) \(\frac{7}{2}\)</p>
<p>(D) 3</p>
Step-by-Step Solution
Key Concept: Apply AM-GM inequality to show the minimum value is 3.
<p><strong>By AM-GM inequality:</strong> \(\frac{a}{b}+\frac{b}{c}+\frac{c}{a} \geq 3\sqrt[3]{\frac{a}{b} \cdot \frac{b}{c} \cdot \frac{c}{a}} = 3\)</p><p>Therefore, the expression can never equal 1.</p>
Correct Answer: A