MathNet 2003 — Part 02 Question 15
Math Olympiad Vault · MathNet 2003 — Part 02
Let $\mathcal{R}$ be the finite region of the plane that is bounded by the $x$ axis and the graph of the $2 x^{2}+5 y=10$ equation curve. Given three points of $\mathcal{R}$, which of the following statements is always true?
at least two of the three points have distance $\geq \frac{\sqrt{5}}{2}$
at least two of the three points have distance $\leq 3$
the sum of the distances between the points is $\leq \frac{9}{2} \sqrt{5}$
the sum of the squares of the distances between the points is $\leq 38$
the product of the distances between points is $\leq 16 \sqrt{5}$.