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MATH / The solutions of x(x−3)=1 may be expressed in the form (a+√(b))/(c) and (a−√(b))/(c), where a, b, and c are prime numbers. Find abc.

Problem

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problem

The solutions of

x(x-3)=1

may be expressed in the form

\frac{a+\sqrt{b}}{c}

and

\frac{a-\sqrt{b}}{c}

, where

a

b

, and

c

are prime numbers. Find

abc

Plain-text mathematical notation (without MathML)

The solutions of x(x−3)=1 may be expressed in the form (a+√(b))/(c) and (a−√(b))/(c), where a, b, and c are prime numbers.  Find abc.

Original LaTeX notation

The solutions of $x(x-3)=1$ may be expressed in the form $\frac{a+\sqrt{b}}{c}$ and $\frac{a-\sqrt{b}}{c}$, where $a$, $b$, and $c$ are prime numbers.  Find $abc$.

level

Level 4

type

Algebra

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task_id: 2e2a52ab-660c-50c9-9ccc-915324139ed1
task_key: algebra--test--2e2a52ab-660c-50c9-9ccc-915324139ed1
task_revision_id: 2
config / split: algebra / test

Official source

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