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MATH / For any two real numbers x and y, define

Problem

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

problem

For any two real numbers xx and y,y, define \[x \star y = ax + by + cxy,\]where a,a, b,b, and cc are constants. It is known that $1 \star 2 = 3,$ $2 \star 3 = 4,$ and there is a non-zero real number dd such that $x \star d = x$ for any real number x.x. What is the value of dd?
Plain-text mathematical notation (without MathML)
For any two real numbers x and y, define
\[x \star y = ax + by + cxy,\]where a, b, and c are constants.  It is known that $1 \star 2 = 3,$ $2 \star 3 = 4,$ and there is a non-zero real number d such that $x \star d = x$ for any real number x.  What is the value of d?
Original LaTeX notation
For any two real numbers $x$ and $y,$ define
\[x \star y = ax + by + cxy,\]where $a,$ $b,$ and $c$ are constants.  It is known that $1 \star 2 = 3,$ $2 \star 3 = 4,$ and there is a non-zero real number $d$ such that $x \star d = x$ for any real number $x.$  What is the value of $d$?

level

Level 4

type

Intermediate Algebra

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Source and history

task_id
b147d141-b4a9-5ecb-af17-705b1eb70518
task_key
intermediate~5falgebra--test--b147d141-b4a9-5ecb-af17-705b1eb70518
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import