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OlympiadBench / 2330 / Determine all triples (x,y,z) of real numbers that satisfy the following…

Problem

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

question

Determine all triples (x,y,z)(x, y, z) of real numbers that satisfy the following system of equations: $$ \begin{aligned} (x-1)(y-2) & =0 \\ (x-3)(z+2) & =0 \\ x+y z & =9 \end{aligned} $$
Plain-text mathematical notation (without MathML)
Determine all triples (x,y,z) of real numbers that satisfy the following system of equations:

$$
\begin{aligned}
(x-1)(y-2) & =0 \\
(x-3)(z+2) & =0 \\
x+y z & =9
\end{aligned}
$$
Original LaTeX notation
Determine all triples $(x, y, z)$ of real numbers that satisfy the following system of equations:

$$
\begin{aligned}
(x-1)(y-2) & =0 \\
(x-3)(z+2) & =0 \\
x+y z & =9
\end{aligned}
$$

answer type

Tuple

is multiple answer

true

language

English

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID
2330
task_id
5e65b436-d313-52d4-bdc4-afb7f3096d53
task_key
OE~5fTO~5fmaths~5fen~5fCOMP--train--2330
task_revision_id
4
config / split
OE_TO_maths_en_COMP / train

Official source

initial import