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Omni-MATH / Let x,y, and z be distinct real numbers that sum to 0. Find the maximum possible value of (xy+yz+zx)/(x²+y²+z²)

Problem

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problem

Let x,yx, y, and zz be distinct real numbers that sum to 0. Find the maximum possible value of xy+yz+zxx2+y2+z2\frac{x y+y z+z x}{x^{2}+y^{2}+z^{2}}
Plain-text mathematical notation (without MathML)
Let x,y, and z be distinct real numbers that sum to 0. Find the maximum possible value of (xy+yz+zx)/(x²+y²+z²)
Original LaTeX notation
Let $x, y$, and $z$ be distinct real numbers that sum to 0. Find the maximum possible value of $$\frac{x y+y z+z x}{x^{2}+y^{2}+z^{2}}$$

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Source and history

task_id
58e5b70e-8113-55ec-884f-424156fc9386
task_key
test--58e5b70e-8113-55ec-884f-424156fc9386
task_revision_id
1
config / split
/ test

Official source

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