A Minimum With a Surprising Constant

★ 9/10Substitution AM-GM inequality Casework

Problem

Let $x, y, z \ge 0$ with at most one of them zero. Find the minimum of

f(x,y,z) = \sqrt{\frac{x^2 + 256yz}{y^2+z^2}} + \sqrt{\frac{y^2 + 256zx}{z^2+x^2}} + \sqrt{\frac{z^2 + 256xy}{x^2+y^2}}.

Answer

Solution

Difficulty	9/10
Topics	Substitution, AM-GM, inequality, Casework

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.