BUILT-IN MATHEMATICA SYMBOL

# NSolve

NSolve[expr, vars]
attempts to find numerical approximations to the solutions of the system expr of equations or inequalities for the variables vars.

NSolve[expr, vars, Reals]
finds solutions over the domain of real numbers.

## Details and OptionsDetails and Options

• The system expr can be any logical combination of:
•  lhs==rhs equations lhs!=rhs inequations or inequalities exprdom domain specifications ForAll[x,cond,expr] universal quantifiers Exists[x,cond,expr] existential quantifiers
• NSolve[{expr1, expr2, ...}, vars] is equivalent to NSolve[expr1&&expr2&&..., vars].
• A single variable or a list of variables can be specified.
• NSolve gives solutions in terms of rules of the form .
• When there are several variables, the solution is given in terms of lists of rules: .
• When there are several solutions, NSolve gives a list of them.
• When a single variable is specified and a particular root of an equation has multiplicity greater than one, NSolve gives several copies of the corresponding solution.
• NSolve[expr, vars] assumes by default that quantities appearing algebraically in inequalities are real, while all other quantities are complex.
• In NSolve[expr, vars, Reals] all variables, parameters, constants, and function values are restricted to be real.
• NSolve[expr&&varsReals, vars, Complexes] solves for real values of variables, but function values are allowed to be complex.
• NSolve deals primarily with linear and polynomial equations.
• The following options can be given:
•  Method Automatic what method should be used WorkingPrecision Automatic precision to be used in computations
• NSolve gives if there are no solutions to the equations.
• NSolve gives if the set of solutions is full dimensional.

## ExamplesExamplesopen allclose all

### Basic Examples (1)Basic Examples (1)

Approximate solutions to a polynomial equation:

 Out[1]=

Approximate real solutions to a polynomial equation:

 Out[2]=

Approximate solutions to a system of polynomial equations:

 Out[3]=

Approximate real solutions to a system of polynomial equations:

 Out[4]=