>> syms x y z
>> eq1=(18*(2*x - 30))/(5*((y - z)^2 + (x - 15)^2)^(1/2)) + (36*x)/(5*((y - 5)^2 + x^2)^(1/2));
>> eq2=(18*(2*y - 10))/(5*((y - 5)^2 + x^2)^(1/2)) + (18*(2*y - 2*z))/(5*((y - z)^2 + (x - 15)^2)^(1/2)) + 36/5;
>> eq3=(141*(2*z - 16))/(10*((z - 8)^2 + 25)^(1/2)) - (18*(2*y - 2*z))/(5*((y - z)^2 + (x - 15)^2)^(1/2));
>> [x,y,z]=solve(eq1,eq2,eq3,'x','y','z')
经过在matlab7.0中尝试,发现没有问题,
x =
1861137696/586981625+2173/1080500*(-3+5*3^(1/2)+30/2173*2173^(1/2))^3-26751/54025*3^(1/2)-160506/117396325*2173^(1/2)+36791/540250*(-3+5*3^(1/2)+30/2173*2173^(1/2))^2
y =
13/2-5/2*3^(1/2)-15/2173*2173^(1/2)
z =
-6519/108050*(-3+5*3^(1/2)+30/2173*2173^(1/2))^2+451757/54025-2173/324150*(-3+5*3^(1/2)+30/2173*2173^(1/2))^3+17834/10805*3^(1/2)+107004/23479265*2173^(1/2)
这里得到的是符号解,转化为数值解；
>> x=subs(x),y=subs(y),z=subs(z)
x =
5.4593
y =
1.8481
z =
7.3564
>> >> syms x y z
>> eq1=(18*(2*x - 30))/(5*((y - z)^2 + (x - 15)^2)^(1/2)) + (36*x)/(5*((y - 5)^2 + x^2)^(1/2));
>> eq2=(18*(2*y - 10))/(5*((y - 5)^2 + x^2)^(1/2)) + (18*(2*y - 2*z))/(5*((y - z)^2 + (x - 15)^2)^(1/2)) + 36/5;
>> eq3=(141*(2*z - 16))/(10*((z - 8)^2 + 25)^(1/2)) - (18*(2*y - 2*z))/(5*((y - z)^2 + (x - 15)^2)^(1/2));
>> [x,y,z]=solve(eq1,eq2,eq3,'x','y','z')
经过在matlab7.0中尝试,发现没有问题,
x =
1861137696/586981625+2173/1080500*(-3+5*3^(1/2)+30/2173*2173^(1/2))^3-26751/54025*3^(1/2)-160506/117396325*2173^(1/2)+36791/540250*(-3+5*3^(1/2)+30/2173*2173^(1/2))^2
y =
13/2-5/2*3^(1/2)-15/2173*2173^(1/2)
z =
-6519/108050*(-3+5*3^(1/2)+30/2173*2173^(1/2))^2+451757/54025-2173/324150*(-3+5*3^(1/2)+30/2173*2173^(1/2))^3+17834/10805*3^(1/2)+107004/23479265*2173^(1/2)
这里得到的是符号解,转化为数值解；
>> x=subs(x),y=subs(y),z=subs(z)
x =
5.4593
y =
1.8481
z =
7.3564
>>