Difference between revisions of "Solve Command"
From GeoGebra Manual
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* 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> | + | * 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>.}} |
+ | ;Solve[ <List of Parametric Equations>, <List of Variables> ] | ||
+ | :Solves a set of parametric equations for a given set of unknown variables and returns a list of all solutions. | ||
+ | :{{example|1=<div> | ||
+ | :*<code><nowiki>Solve[{(x, y) = (3, 2) + t (5, 1), (x, y) = (4, 1) + s (1, -1)}, {x, y, t, s}]</nowiki></code> yields ''<nowiki>{{x = 3, y = 2, t = 0, s = -1}}</nowiki>''.</div>}} | ||
+ | {{note|1= | ||
+ | * Solving parametric equations is available from GeoGebra 4.4. | ||
* See also [[Solutions Command]].}} | * See also [[Solutions Command]].}} |
Revision as of 13:19, 12 September 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.
- 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)]]
.
- Solve[ <List of Parametric Equations>, <List of Variables> ]
- Solves a set of parametric equations for a given set of unknown variables and returns a list of all solutions.
- Example:
Solve[{(x, y) = (3, 2) + t (5, 1), (x, y) = (4, 1) + s (1, -1)}, {x, y, t, s}]
yields {{x = 3, y = 2, t = 0, s = -1}}.
Note:
- Solving parametric equations is available from GeoGebra 4.4.
- See also Solutions Command.