Difference between revisions of "Solve Command"

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(<code> Solve[TrigExpand[sin(5/4 π+x)-cos(x-3/4 π)=sqrt(6) * cos(x)-sqrt(2)]] </code>)
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{{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.
 +
* Sometimes you need to do some manipulation to allow the automatic solver to work, for example <code> Solve[TrigExpand[sin(5/4 π+x)-cos(x-3/4 π)=sqrt(6) * cos(x)-sqrt(2)]] </code>
 
* See also [[Solutions Command]].}}
 
* See also [[Solutions Command]].}}

Revision as of 15:45, 22 May 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 = 2
  • Solve[{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.
  • Sometimes you need to do some manipulation to allow the automatic solver to work, for example Solve[TrigExpand[sin(5/4 π+x)-cos(x-3/4 π)=sqrt(6) * cos(x)-sqrt(2)]]
  • See also Solutions Command.
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