benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Triangle ABC is inscribed in a circle of radius 2 with ∠ABC≥90^(∘), and x is a real number satisfying the equation x⁴+ax³+bx²+cx+1=0, where a=BC, b=CA, c=AB. Find all possible valu…

Problem

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

problem

Triangle ABCABC is inscribed in a circle of radius 2 with ∠ABC≥90∘\angle ABC \geq 90^\circ, and xx is a real number satisfying the equation x4+ax3+bx2+cx+1=0x^4 + ax^3 + bx^2 + cx + 1 = 0, where a=BCa=BC, b=CAb=CA, c=ABc=AB. Find all possible values of xx.
Plain-text mathematical notation (without MathML)
Triangle ABC is inscribed in a circle of radius 2 with ∠ABC≥90^(∘), and x is a real number satisfying the equation x⁴+ax³+bx²+cx+1=0, where a=BC, b=CA, c=AB. Find all possible values of x.
Original LaTeX notation
Triangle $ABC$ is inscribed in a circle of radius 2 with $\angle ABC \geq 90^\circ$, and $x$ is a real number satisfying the equation $x^4 + ax^3 + bx^2 + cx + 1 = 0$, where $a=BC$, $b=CA$, $c=AB$. Find all possible values of $x$.

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
79153563-bd1b-5da7-b15a-736f4ecfd240
task_key
test--79153563-bd1b-5da7-b15a-736f4ecfd240
task_revision_id
1
config / split
/ test

Official source

initial import