用matlab求解一个三元二次方程组 MATLAB 解三元二次方程
matlab\u6c42\u89e3\u4e09\u5143\u4e8c\u6b21\u65b9\u7a0b\u7ec4x1=-226.11;
y1=238.802;
z1=-1577;
x2=223.1317;
y2=201.5533;
z2=-1577;
x3=-277.2719;
y3=-202.0605;
z3=-1577;
syms t1 t2 t3
eq1=(t1*x1-t2*x2)^2+(t1*y1-t2*y2)^2+(t1*z1-t2*z2)^2-532.8689^2;
eq2=(t1*x1-t3*x3)^2+(t1*y1-t3*y3)^2+(t1*z1-t3*z3)^2-532.8689^2;
eq3=(t3*x3-t2*x2)^2+(t3*y3-t2*y2)^2+(t3*z3-t2*z2)^2-753.5904^2;
[t1 t2 t3]=solve(eq1,eq2,eq3,'t1','t2','t3')
\u697c\u4e3b\u6211\u7528solve\u53ef\u4ee5\u89e3\u51fa\u89e3\u6765\uff0c\u4f60\u53c2\u8003\u4e00\u4e0b
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\u82e5P1=P2=P3\u90a3\u4e48\uff0c\u697c\u4e3b\u7684\u95ee\u9898\u5b9e\u9645\u662f\u627e\u8fd9\u4e09\u4e2a\u70b9\u7684\u5706\u5fc3\uff0c\u53ea\u6709\u4e00\u4e2a\u89e3\u3002\u6240\u4ee5\u80af\u5b9a\u662f\u4e09\u5143\u4e00\u6b21\u7684\uff0c\u56e0\u4e3a\u8fd9\u6837\u7684\u5706\u5fc3\u53ea\u6709\u4e00\u4e2a\u3002\uff081,2,3\u70b9\u4e0d\u5728\u540c\u4e00\u76f4\u7ebf\u4e0a\uff09\u3002
\u5f53\u7136\u5982\u679cp1!=P2!=P3\u4e5f\u53ef\u4ee5\u89e3\uff0c\u5e76\u4e14\u4e5f\u53ea\u6709\u4e00\u4e2a\u89e3\uff0c\u4e0d\u8fc7\u5c31\u4e0d\u662f\u4e00\u4e2a\u5706\uff0c\u6ca1\u6709\u8fd9\u4e48\u597d\u7406\u89e3\u3002\u5982\u679c\u8fd8\u6709\u4e0d\u660e\u767d\u7684\u53ef\u4ee5\u8054\u7cfb\u6211\u3002
\u89e3\u8fd9\u6837\u7684\u95ee\u9898\u8fd8\u7528\u52a8matlab\uff1f
\u8865\u5145\u8bf4\u660e\uff1a\u6211\u8bd5\u4e86\u4e00\u4e0b\uff0c\u786e\u5b9e\u52a8\u624b\u89e3\u4e86\u4e00\u4e0b\u65b9\u7a0b\u7ec4\uff0c\u5176\u5b9e\u8fd8\u662f\u6709\u70b9\u95ee\u9898\u7684\uff0c\u4e3b\u8981\u662f\u5f97\u5230\u7684\u89e3\u8bef\u5dee\u592a\u5927\u3002\u6bd4\u59821400mm\u7684\u6807\u51c6\u89e3\uff0c\u5b9e\u9645\u5f97\u5230\u7684\u7b54\u6848\u53ef\u80fd\u662f1380-1420\u4e4b\u95f4\u3002
由于该三元二次方程组有多个解，每组x,y,z各有6个，所以其图像如下所示。
实现代码：
a=0.2;
b0=[0.1:0.1:10];
for i=1:length(b0)
syms x y z
b=b0(i);
[x,y,z]=vpasolve(a*(x^2+y^2)+(1-2*a)*x+(a-1)-2*b*z==0,a*y*(x+z)+(1-2*a)*y-b*z==0,a*(y^2+z^2)+(1-2*a)*z+(a-1)==0);
y0(i,:)=y;
end
plot(y0,b0,'.-')
xlabel('y'),ylabel('b')
如为实数解的话，还应去掉复数解。
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