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MATH / Let a, b, and c be real numbers such that ab+ac+bc=0 and (a+b+c+1)²=abc. Find all possible values of (ab−c)(ac−b)(bc−a).Enter the possible values, separated by commas. For example,…

Problem

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problem

Let a,a, b,b, and cc be real numbers such that ab+ac+bc=0ab + ac + bc = 0 and (a+b+c+1)2=abc.(a + b + c + 1)^2 = abc. Find all possible values of (ab−c)(ac−b)(bc−a).(ab - c)(ac - b)(bc - a).Enter the possible values, separated by commas. For example, if you think the possible values are 3, 4, and 5, enter "3, 4, 5", without the quotation marks.
Plain-text mathematical notation (without MathML)
Let a, b, and c be real numbers such that ab+ac+bc=0 and (a+b+c+1)²=abc.  Find all possible values of
(ab−c)(ac−b)(bc−a).Enter the possible values, separated by commas.  For example, if you think the possible values are 3, 4, and 5, enter "3, 4, 5", without the quotation marks.
Original LaTeX notation
Let $a,$ $b,$ and $c$ be real numbers such that $ab + ac + bc = 0$ and $(a + b + c + 1)^2 = abc.$  Find all possible values of
\[(ab - c)(ac - b)(bc - a).\]Enter the possible values, separated by commas.  For example, if you think the possible values are 3, 4, and 5, enter "3, 4, 5", without the quotation marks.

level

Level 5

type

Intermediate Algebra

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Source and history

task_id
e7cb2dcd-24fa-5243-aff6-c0b4081986a0
task_key
intermediate~5falgebra--test--e7cb2dcd-24fa-5243-aff6-c0b4081986a0
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import