Question

Let \(a, b \in \mathbb{R}\) and \(0 \le a < b\), then:

• A. \(\frac{1}{a} < \frac{1}{b}\)
• B. \(ab > b^2\)
• C. \(ab < a^2\)
• D. \(a^2 < ab\)

Hint:

To quickly verify algebraic inequalities, plug in simple positive values that satisfy the condition.
Let \(a = 2\) and \(b = 3\). Then:
- \(a^2 = 4\) and \(ab = 6\).
Since \(4 < 6\) is true, \(a^2 < ab\) is the correct inequality.

Answer 1

The Correct Option is D