Difference between revisions of "Solutions Command"
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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|geogebra}} | <noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|geogebra}} | ||
==CAS Syntax== | ==CAS Syntax== | ||
| − | ;Solutions | + | ;Solutions( <Equation> ) |
: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>Solutions[x^2 = 4x]</nowiki></code> yields ''{0, 4}'', the solutions of ''x<sup>2</sup> = 4x''.</div>}} | :{{example|1=<div><code><nowiki>Solutions[x^2 = 4x]</nowiki></code> yields ''{0, 4}'', the solutions of ''x<sup>2</sup> = 4x''.</div>}} | ||
| − | ;Solutions | + | ;Solutions( <Equation>, <Variable> ) |
:Solves an equation for a given unknown variable and returns a list of all solutions. | :Solves an equation for a given unknown variable and returns a list of all solutions. | ||
:{{example|1=<div><code><nowiki>Solutions[x * a^2 = 4a, a]</nowiki></code> yields {<math>\frac{4}{x},0</math>}, the solutions of ''xa<sup>2</sup> = 4a''.</div>}} | :{{example|1=<div><code><nowiki>Solutions[x * a^2 = 4a, a]</nowiki></code> yields {<math>\frac{4}{x},0</math>}, the solutions of ''xa<sup>2</sup> = 4a''.</div>}} | ||
| − | ;Solutions | + | ;Solutions( <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> | ||
Revision as of 17:16, 7 October 2017
CAS Syntax
- Solutions( <Equation> )
- Solves a given equation for the main variable and returns a list of all solutions.
- Example:
Solutions[x^2 = 4x]yields {0, 4}, the solutions of x2 = 4x.
- Solutions( <Equation>, <Variable> )
- Solves an equation for a given unknown variable and returns a list of all solutions.
- Example:
Solutions[x * a^2 = 4a, a]yields {\frac{4}{x},0}, the solutions of xa2 = 4a.
- Solutions( <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:
Solutions[{x = 4 x + y , y + x = 2}, {x, y}]yields {{-1, 3}}, the sole solution of x = 4x + y and y + x = 2, displayed as \begin{pmatrix}-1&3\end{pmatrix}.Solutions[{2a^2 + 5a + 3 = b, a + b = 3}, {a, b}]yields {{-3, 6}, {0, 3}}, displayed as \begin{pmatrix}-3&6\\0&3\end{pmatrix}.
- Note:
- Sometimes you need to do some manipulation to allow the automatic solver to work, for example
Solutions[TrigExpand[sin(5/4 π + x) - cos(x - 3/4 π) = sqrt(6) * cos(x) - sqrt(2)]] - See also Solve Command.
- Sometimes you need to do some manipulation to allow the automatic solver to work, for example
