A Minimax of Three

Problem

Let $\max\{a, b, c\}$ denote the largest of the real numbers $a, b, c$ . For $x, y, z > 0$ , find the minimum value of

\max\left\{xz + \frac{1}{y},\; x + \frac{1}{yz},\; \frac{y}{x} + \frac{1}{z}\right\}.

Answer

Solution

Difficulty	7/10
Topics	AM-GM, inequality

Whiteboard

Your sketch is saved only in this browser. To share it, export your drawing as an image (whiteboard menu → Export as → PNG), then upload that image in the comments below.

Discussion

Ask questions, share alternate solutions, and use LaTeX freely.

0 comments

No comments yet.