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OlympiadBench / 2203 / Find all triples (a,b,c) of real numbers such that ab+bc+ ca=1 and

Problem

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

answer type

Tuple

is multiple answer

true

language

English

question

Find all triples

(a, b, c)

of real numbers such that

a b+b c+

c a=1

and

a^{2} b+c=b^{2} c+a=c^{2} a+b \text {. }

Plain-text mathematical notation (without MathML)

Find all triples (a,b,c) of real numbers such that ab+bc+ ca=1 and

a²b+c=b²c+a=c²a+b.

Original LaTeX notation

Find all triples $(a, b, c)$ of real numbers such that $a b+b c+$ $c a=1$ and

$$
a^{2} b+c=b^{2} c+a=c^{2} a+b \text {. }
$$

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 2203
task_id: 0a4d3a15-6eae-575f-8d23-b57fcbe2f307
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--2203
task_revision_id: 1
config / split: OE_TO_maths_en_COMP / train

Official source

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