benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / In triangle ABC,AB=32,AC=35, and BC=x. What is the smallest positive integer x such that 1+cos²A,cos²B, and cos²C form the sides of a non-degenerate triangle?

Problem

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

problem

In triangle ABC,AB=32,AC=35ABC, AB=32, AC=35, and BC=xBC=x. What is the smallest positive integer xx such that 1+cos2A,cos2B1+\cos^{2}A, \cos^{2}B, and cos2C\cos^{2}C form the sides of a non-degenerate triangle?
Plain-text mathematical notation (without MathML)
In triangle ABC,AB=32,AC=35, and BC=x. What is the smallest positive integer x such that 1+cos²A,cos²B, and cos²C form the sides of a non-degenerate triangle?
Original LaTeX notation
In triangle $ABC, AB=32, AC=35$, and $BC=x$. What is the smallest positive integer $x$ such that $1+\cos^{2}A, \cos^{2}B$, and $\cos^{2}C$ form the sides of a non-degenerate triangle?

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
a330d38e-e9c3-542e-99c9-5cb962a2cd71
task_key
test--a330d38e-e9c3-542e-99c9-5cb962a2cd71
task_revision_id
1
config / split
/ test

Official source

initial import