求解三元二次方程4（x^2 +y^2）-3x^2=4c^2(x^2+y^2)+c^2=10cx/3

2019-05-28

求解三元二次方程
4（x^2 +y^2）-3x^2=4c^2
(x^2+y^2)+c^2=10cx/3

优质解答

我用的Mathematica解的,
NSolve[{4 (x^2 + y^2) - 3 x^2 == 4 c^2, (x^2 + y^2) + c^2 ==
10 c x/3, x^2 + y^2 == 31/9}, {x, y, c}]
得到：
{{c -> -1.57789, y -> -1.4736, x -> -1.12825},
{c -> -1.57789, y -> 1.4736, x -> -1.12825},
{c -> 1.57789, y -> -1.4736, x -> 1.12825},
{c -> 1.57789, y -> 1.4736, x -> 1.12825},
{c -> 0.548922, y -> 0. - 0.863941 I, x -> 2.04715},
{c -> 0.548922, y -> 0. + 0.863941 I, x -> 2.04715},
{c -> -0.548922, y -> 0. - 0.863941 I, x -> -2.04715},
{c -> -0.548922, y -> 0. + 0.863941 I, x -> -2.04715}}
如果x,y,c都大于0,你得到,x=1.12825, y=1.4736, c=1.57789 我用的Mathematica解的,
NSolve[{4 (x^2 + y^2) - 3 x^2 == 4 c^2, (x^2 + y^2) + c^2 ==
10 c x/3, x^2 + y^2 == 31/9}, {x, y, c}]
得到：
{{c -> -1.57789, y -> -1.4736, x -> -1.12825},
{c -> -1.57789, y -> 1.4736, x -> -1.12825},
{c -> 1.57789, y -> -1.4736, x -> 1.12825},
{c -> 1.57789, y -> 1.4736, x -> 1.12825},
{c -> 0.548922, y -> 0. - 0.863941 I, x -> 2.04715},
{c -> 0.548922, y -> 0. + 0.863941 I, x -> 2.04715},
{c -> -0.548922, y -> 0. - 0.863941 I, x -> -2.04715},
{c -> -0.548922, y -> 0. + 0.863941 I, x -> -2.04715}}
如果x,y,c都大于0,你得到,x=1.12825, y=1.4736, c=1.57789