Equation

2017-08-20T08:18:06Z

122.176.186.201: delete4]u78667589

{{for|a chemical type of equation|Chemical equation}}
A mathematical '''equation''' is an expression containing at least one [[variable]] (=unknown value) and an "[[equals sign]]" ( = ) with a mathematical expression on each side of it.<ref>An equation is an equality that is true only for certain values of the variable. [http://www.themathpage.com/atrig/trigonometric-identities.htm Trigonometric identities. Topics in trigonometry.]</ref><ref>"A statement of equality between two expressions. Equations are of two types, '''identities''' and '''conditional equations''' (or usually simply "equations")". « ''Equation'' », in ''Mathematics Dictionary'', Glenn James et Robert C. James (éd.), Van Nostrand, 1968, 3 ed. 1st ed. 1948, p. 131.</ref><ref>Une équation est une égalité entre deux expressions mathématiques, donc une formule de la forme A = B, où les deux membres A et B de l'équation sont des expressions où figurent une ou plusieurs variables, représentées par des lettres. [http://www.universalis.fr/encyclopedie/equation-mathematique/ ÉQUATION, mathématique - Encyclopædia Universalis]</ref> The equals sign says that both sides are exactly [[equal|the same]] value. An equation can be as simple as x=0, or as hard as 4(3y^99)+76=42÷3x or harder.

There are two kinds of mathematical equations:
* The kind of equation that is either true or false; these are also called identities. For example:
: <math>2 \cdot (x+4)=2x+8 \rightarrow true</math>
* The kind of equation that lets you [[Calculator|calculate]] the [[value]] of one or several [[variable]]s. The equation is only true if the variable(s) have that value. For example:
: <math>2 \cdot x=8 \rightarrow x=4</math>

The second kind is often used to [[solve]] problems in which you have to know the value of some variables. For example,
: <math> \text{if}\, 2x = 8, \, x = \frac{8}{2} = 4. </math>

The second kind of equation is used in [[algebra]]. For example, to [[solve]] the equation 2x = 8 by finding x you would follow an algebraic [[rule]]. Then you can work out that x = 4.

== Types of equations ==
Equations can be classified by the types of [[Operation (mathematics)|operations]] and [[Quantity|quantities]] involved. Some types of equations are:
* An [[algebraic equation]] is an equation in which both sides are [[polynomial]]s. These are further classified by [[Degree of a polynomial|degree]]:
** [[linear equation]] for degree one
** [[quadratic equation]] for degree two
** [[cubic equation]] for degree three
** [[quartic equation]] for degree four
** [[quintic equation]] for degree five
* A [[Diophantine equation]] is an equation where the [[Unknown (math)|unknowns]] are required to be [[integer]]s
* A [[differential equation]] is a [[functional equation]] involving [[Derivative (mathematics)|derivatives]] of the unknown functions

== Related pages ==
* [[Formula]]

==References==
{{reflist}}

[[Category:Equations| ]]

{{math-stub}}

TCS Wiki - User contributions [en]

Equation