Difference between revisions of "Solve Command"
From GeoGebra Manual
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{{command|geogebra}} | {{command|geogebra}} | ||
==CAS Syntax== | ==CAS Syntax== | ||
| − | ;Solve[ <Equation> ] | + | ;Solve[ <Equation in x> ] |
:Solves a given equation for the main variable and returns a list of all solutions. | :Solves a given equation for the main variable and returns a list of all solutions. | ||
:{{example|1=<div><code><nowiki>Solve[x^2 = 4x]</nowiki></code> yields ''{x = 4, x = 0}'', the solutions of ''x<sup>2</sup> = 4x''.</div>}} | :{{example|1=<div><code><nowiki>Solve[x^2 = 4x]</nowiki></code> yields ''{x = 4, x = 0}'', the solutions of ''x<sup>2</sup> = 4x''.</div>}} | ||
| − | |||
;Solve[ <Equation>, <Variable> ] | ;Solve[ <Equation>, <Variable> ] | ||
| − | :Solves an equation for a given unknown variable and returns a list of all | + | :Solves an equation for a given unknown variable and returns a list of all solutions. |
| − | :{{example|1=<div><code><nowiki>Solve[x * a^2 = 4a, a]</nowiki></code> yields <math>\{a = \frac{4}{x}, a = 0\}</math>, the solutions of '' | + | :{{example|1=<div><code><nowiki>Solve[x * a^2 = 4a, a]</nowiki></code> yields <math>\{a = \frac{4}{x}, a = 0\}</math>, the solutions of ''xa<sup>2</sup> = 4a''.</div>}} |
| − | |||
;Solve[ <List of Equations>, <List of Variables> ] | ;Solve[ <List of Equations>, <List of Variables> ] | ||
:Solves a set of equations for a given set of unknown variables and returns a list of all solutions. | :Solves a set of equations for a given set of unknown variables and returns a list of all solutions. | ||
:{{examples|1=<div> | :{{examples|1=<div> | ||
| − | :* <code><nowiki>Solve[{x = 4 x + y , y + x = 2}, {x, y}]</nowiki></code> yields ''<nowiki> | + | :*<code><nowiki>Solve[{x = 4 x + y , y + x = 2}, {x, y}]</nowiki></code> yields ''<nowiki>( x = -1, y = 3 )</nowiki>'', the sole solution of ''x = 4x + y'' and ''y + x = 2'' |
| − | :* <code><nowiki>Solve[{2a^2 + 5a + 3 = b, a + b = 3}, {a, b}]</nowiki></code> yields ''{{a = 0, b = 3}, {a = -3, b = 6}}''.</div>}} | + | :*<code><nowiki>Solve[{2a^2 + 5a + 3 = b, a + b = 3}, {a, b}]</nowiki></code> yields ''{{a = 0, b = 3}, {a = -3, b = 6}}''.</div>}} |
| − | |||
{{note|1= | {{note|1= | ||
* The right hand side of equations (in any of the above syntaxes) can be omitted. If the right hand side is missing, it is treated as 0. | * The right hand side of equations (in any of the above syntaxes) can be omitted. If the right hand side is missing, it is treated as 0. | ||
* See also [[Solutions Command]].}} | * See also [[Solutions Command]].}} | ||
Revision as of 10:37, 26 March 2013
CAS Syntax
- Solve[ <Equation in x> ]
- Solves a given equation for the main variable and returns a list of all solutions.
- Example:
Solve[x^2 = 4x]yields {x = 4, x = 0}, the solutions of x2 = 4x.
- Solve[ <Equation>, <Variable> ]
- Solves an equation for a given unknown variable and returns a list of all solutions.
- Example:
Solve[x * a^2 = 4a, a]yields \{a = \frac{4}{x}, a = 0\}, the solutions of xa2 = 4a.
- Solve[ <List of Equations>, <List of Variables> ]
- Solves a set of equations for a given set of unknown variables and returns a list of all solutions.
- Examples:
Solve[{x = 4 x + y , y + x = 2}, {x, y}]yields ( x = -1, y = 3 ), the sole solution of x = 4x + y and y + x = 2Solve[{2a^2 + 5a + 3 = b, a + b = 3}, {a, b}]yields {{a = 0, b = 3}, {a = -3, b = 6}}.
Note:
- The right hand side of equations (in any of the above syntaxes) can be omitted. If the right hand side is missing, it is treated as 0.
- See also Solutions Command.
