Difference between revisions of "Solutions Command"

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<noinclude>{{Manual Page|version=4.0}}</noinclude>
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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|geogebra}}
{{command|CAS}}
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==CAS Syntax==
;Solutions[ <Equation> ]
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;Solutions( <Equation> )
:Solves a given equation (or a set of equations) for the variable x and returns a list of all solutions.
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: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> gives ''{{4}, {0}}'', the solutions of ''x<sup>2</sup> = 4x''.</div>}}
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:{{example|1=<code><nowiki>Solutions(x^2 = 4x)</nowiki></code> yields ''{0, 4}'', the solutions of ''x<sup>2</sup> = 4x''.}}
;Solutions[ <Equation>, <Variable> ]
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;Solutions( <Equation>, <Variable> )
:Solves an equation (or a set of equations) for a given unknown variable (or set of variables) and returns a list of all solutions.
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:Solves an equation for a given unknown variable and returns a list of all solutions.
:{{Example|1=<div><code><nowiki>Solutions[{x = 4 x + y , y + x = 2}, {x, y}]</nowiki></code> gives ''{ {-1, 3} }'', the sole solution of ''x = 4x + y'' and ''y + x = 2''.</div>}}
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:{{example|1=<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''.}}
{{Note|See also [[Solve Command]].}}
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;Solutions( <List of Equations>, <List of Variables> )
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:Solves a set of equations for a given set of unknown variables and returns a list of all solutions.
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:{{examples|1=<div>
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:* <code><nowiki>Solutions({x = 4 x + y , y + x = 2}, {x, y})</nowiki></code> yields ''&#123;&#123;-1, 3&#125;&#125;'', the sole solution of ''x = 4x + y'' and ''y + x = 2'', displayed as <math>\begin{pmatrix}-1&3\end{pmatrix}</math>.
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:* <code><nowiki>Solutions({2a^2 + 5a + 3 = b, a + b = 3}, {a, b})</nowiki></code> yields ''&#123;&#123;-3, 6}, {0, 3&#125;&#125;'', displayed as <math>\begin{pmatrix}-3&6\\0&3\end{pmatrix}</math>.</div>}}  
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:{{note|1=
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:* Sometimes you need to do some manipulation to allow the automatic solver to work, for example  <code> Solutions(TrigExpand(sin(5/4 π + x) - cos(x - 3/4 π) = sqrt(6) * cos(x) - sqrt(2))) </code>
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:* See also [[Solve Command]].}}

Revision as of 10:04, 12 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.
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