benchmarks.wiki

benchmarks.wiki / Public workspace

MATH / Let a, b, c be positive real numbers such that both

Problem

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

problem

Let a,a, b,b, cc be positive real numbers such that both x4+ax3+bx2+cx+1x^4 + ax^3 + bx^2 + cx + 1and x4+2ax3+2bx2+2cx+1x^4 + 2ax^3 + 2bx^2 + 2cx + 1are both squares of polynomials. Find a+b+c.a + b + c.
Plain-text mathematical notation (without MathML)
Let a, b, c be positive real numbers such that both
x⁴+ax³+bx²+cx+1and
x⁴+2ax³+2bx²+2cx+1are both squares of polynomials.  Find a+b+c.
Original LaTeX notation
Let $a,$ $b,$ $c$ be positive real numbers such that both
\[x^4 + ax^3 + bx^2 + cx + 1\]and
\[x^4 + 2ax^3 + 2bx^2 + 2cx + 1\]are both squares of polynomials.  Find $a + b + c.$

level

Level 4

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
bd7b046c-ff8e-52a0-b67d-103c26879165
task_key
intermediate~5falgebra--test--bd7b046c-ff8e-52a0-b67d-103c26879165
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import