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Math Definitions - Letter E

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Extraneous Solution

Definition of Extraneous Solution

Sometimes the tricks we use to find the solutions of equations introduce new solutions that aren't actually solutions of the original equation. We call these extraneous solutions.

As a silly example (you would never do this!), suppose you were asked to solve the equation \(x + 3 = 2\). If you squared both sides, you would get

\(\begin{align*} (x + 3)^2 &= 2 \\ x^2 + 6x + 9 &= 4\\ x^2 + 6x + 5 &= 0\\ (x + 5)(x + 1)&= 0\\ x&= -5 \text{ and }x = -1. \end{align*} \)

One of these solutions doesn't satisfy the original equation! When we plug in \(x = -5\), we get \(-5 + 3 = -2 \neq 2\). So, \(x = -5\) is an extraneous solution to this equation.

When you've solved an equation, it's always a good idea to check that all the solutions you have found are actually solutions of the original equation.

Description

The aim of this dictionary is to provide definitions to common mathematical terms. Students learn a new math skill every week at school, sometimes just before they start a new skill, if they want to look at what a specific term means, this is where this dictionary will become handy and a go-to guide for a student.

Audience

Year 1 to Year 12 students

Learning Objectives

Learn common math terms starting with letter E

Author: Subject Coach
Added on: 6th Feb 2018

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