Maple/方程求解

二次多項式方程

$f:=a*x^{2}+b*x+c;$

求解 f=0;

solve(f,x);

$(1/2)*(-b+{\sqrt {(}}b^{2}-4*a*c))/a,-(1/2)*(b+{\sqrt {(}}b^{2}-4*a*c))/a$ ${\displaystyle }$

三次多項式方程

$f:=5*x^{3}+6*x^{2}+7*x+8$

solve(f，x);

$-(1/15)*(1971+15*{\sqrt {(}}18726))^{(}1/3)+23/(5*(1971+15*{\sqrt {(}}18726))^{(}1/3))-2/5,$

$(1/30)*(1971+15*{\sqrt {(}}18726))^{(}1/3)-23/(10*(1971+15*{\sqrt {(}}18726))^{(}1/3))-2/5+(1/2*I)*{\sqrt {(}}3)*(-(1/15)*(1971+15*{\sqrt {(}}18726))^{(}1/3)-23/(5*(1971+15*{\sqrt {(}}18726))^{(}1/3)))$,

$(1/30)*(1971+15*{\sqrt {(}}18726))^{(}1/3)-23/(10*(1971+15*{\sqrt {(}}18726))^{(}1/3))-2/5-(1/2*I)*{\sqrt {(}}3)*(-(1/15)*(1971+15*{\sqrt {(}}18726))^{(}1/3)-23/(5*(1971+15*{\sqrt {(}}18726))^{(}1/3)))$ ${\displaystyle }$ ${\displaystyle }$ ${\displaystyle }$ ${\displaystyle }$ ${\displaystyle }$ ${\displaystyle }$

高次多項式方程

f := x^7+3*x = 7;

solve(f,x);

RootOf($Z^{7}+3Z-7$, index = 1),

RootOf($Z^{7}+3Z-7$, index = 2),

RootOf($Z^{7}+3Z-7$, index = 3),

RootOf($Z^{7}+3Z-7$, index = 4),

RootOf($Z^{7}+3Z-7$, index = 5),

RootOf($Z^{7}+3Z-7$, index = 5),

RootOf($Z^{7}+3Z-7$, index =7),

evalf(%);

• (1.1922047171828134),
• (0.8658388666792263) + (0.9230818802764879) I,
• (0.2099602786426775) + (1.3442579297631496) I,
• (1.2519809466279554) + (0.6424819505558892) I,
• (1.2519809466279554) - (0.6424819505558892) I,
• (0.2099602786426775) - (1.3442579297631496) I,
• (0.8658388666792263) - (0.9230818802764879) I

三角函數方程

f := sin(x)^3+5*cosh(x) = 0;

$sin^{3}(x)+5cosh(x)=0$

> solve(f, x);

RootOf($sin^{3}(Z)-arccosh({\frac {-1}{5}}sin(Z)$))

> evalf(%);

0.2873691672 - 1.111497506 I

方程組

> p1 := x*y*z-x*y^2-z-x-y; p2 := x*z-x^2-z-y+x; p3 := z^2-x^2-y^2;

> sys := {p1, p2, p3};

> var := {x, y, z};

> solve(sys, var);

： {x = 0, y = y, z = -y}, {x = 3, y = 4, z = 5}, {x = 1, y = 0, z = -1}

三角函數方程組

> f1 := cos(x)+sin(3*y)+tan(5*z) = 0;

> f2 := cos(3*z)+tan(3*y^2)-sin(2*z^3) = 33;

> f3 := tan(4*x+y)-sin(5*y-4*z) = 2*x;

> sys1 := {f1, f2, f3};

> var1 := {x, y, z};

{x, y, z}

> fsolve(sys1, var1);

{x = -10.77771790, y = -2.397849343, z = -7.382158103}