benchmarks.wiki

benchmarks.wiki / Public workspace

MATH / Given that x, y, z>0 and xyz=1, find the range of all possible values of (x³+y³+z³−x^(−3)−y^(−3)−z^(−3))/(x+y+z−x^(−1)−y^(−1)−z^(−1)).

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Given that x,x, y,y, z>0z > 0 and xyz=1,xyz = 1, find the range of all possible values of x3+y3+z3−x−3−y−3−z−3x+y+z−x−1−y−1−z−1.\frac{x^3 + y^3 + z^3 - x^{-3} - y^{-3} - z^{-3}}{x + y + z - x^{-1} - y^{-1} - z^{-1}}.
Plain-text mathematical notation (without MathML)
Given that x, y, z>0 and xyz=1, find the range of all possible values of
(x³+y³+z³−x^(−3)−y^(−3)−z^(−3))/(x+y+z−x^(−1)−y^(−1)−z^(−1)).
Original LaTeX notation
Given that $x,$ $y,$ $z > 0$ and $xyz = 1,$ find the range of all possible values of
\[\frac{x^3 + y^3 + z^3 - x^{-3} - y^{-3} - z^{-3}}{x + y + z - x^{-1} - y^{-1} - z^{-1}}.\]

level

Level 5

type

Intermediate Algebra

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
c5818b72-9559-53de-95c8-2fcc1ed2642a
task_key
intermediate~5falgebra--test--c5818b72-9559-53de-95c8-2fcc1ed2642a
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import