Unable to find explicit solution

syms c l1 h1 d1 d2 d3 d4 l2 h2 k3 l3 h3 h4 k4 l4 B

q1=1/(d3^2)==((h3^2/d1^2*h1^2)+(k3^2)/(d2^2*l2^2)+l3^2/(c^2*sin(B)^2)-(2*h3*l3*cos(B))/(d1*h1*c*sin(B)));

q2=1/(d4^2)==((h4^2/d1^2*h1^2)+(k4^2)/(d2^2*l2^2)+l4^2/(c^2*sin(B)^2)-(2*h4*l4*cos(B))/(d1*h1*c*sin(B)));

                sol=solve([q1, q2], [c, B]);
                csol=sol.c
                Bsol=sol.B
the Ans is 'Unable to find explicit solution'

but when I use value

the Ans can be found

h1=1; d3=10; d4=15; h3=2; h4=1; d1=24; k3=3; k4=2; d2=18; l2=2; l3=1; l4=3;

syms c B

q1=1/(d3^2)==((h3^2/d1^2*h1^2)+(k3^2)/(d2^2*l2^2)+l3^2/(c^2*sin(B)^2)-(2*h3*l3*cos(B))/(d1*h1*c*sin(B)));

q2=1/(d4^2)==((h4^2/d1^2*h1^2)+(k4^2)/(d2^2*l2^2)+l4^2/(c^2*sin(B)^2)-(2*h4*l4*cos(B))/(d1*h1*c*sin(B)));

                sol=solve([q1, q2], [c, B]);
                csol=sol.c
                Bsol=sol.B
csol =

   (919795581000*(- (38460*21210^(1/2))/149167 - 5603167/149167)^(1/2))/669312329 + (81000*(- (38460*21210^(1/2))/149167 - 5603167/149167)^(3/2))/4487
 - (919795581000*(- (38460*21210^(1/2))/149167 - 5603167/149167)^(1/2))/669312329 - (81000*(- (38460*21210^(1/2))/149167 - 5603167/149167)^(3/2))/4487
       (919795581000*((38460*21210^(1/2))/149167 - 5603167/149167)^(1/2))/669312329 + (81000*((38460*21210^(1/2))/149167 - 5603167/149167)^(3/2))/4487
     - (919795581000*((38460*21210^(1/2))/149167 - 5603167/149167)^(1/2))/669312329 - (81000*((38460*21210^(1/2))/149167 - 5603167/149167)^(3/2))/4487

Bsol =

 -2*atan((- (38460*21210^(1/2))/149167 - 5603167/149167)^(1/2))
  2*atan((- (38460*21210^(1/2))/149167 - 5603167/149167)^(1/2))
   -2*atan(((38460*21210^(1/2))/149167 - 5603167/149167)^(1/2))
    2*atan(((38460*21210^(1/2))/149167 - 5603167/149167)^(1/2))

how can i show the Ans with symbol? thanks

Answer 1

[Dimitris Kalogiros]

Your query is a mathematical issue and not a matlab issue.

Let me give you an example...

Supose you want to solve analytically a 6th degree polynomial equation:

a*x^6 + b*x^5 + c*x^4 + d*x^3 + e*x^2 + f*x^1 + g =0

There is no analytical formulla for every value of coefficients a,b,c,d,e,f,g

But for some sets of these coefficients, there is indeed a compact way to find the solution:

2*x^6 -2*x^4 - 8*x^2 + 8 = 0

2(x^6 - x^4 -4*x^2 + 4) = 0

2 * (x^2 - 1) * (x^4 - 4 ) = 0

2 * (x-1) * (x+1) * (x^2 - 2) * (x^2 +2) = 0

2 * (x-1) * (x+1) * (x - sqrt(2) ) * (x + sqrt(2) ) * ( x^2 +2 ) = 0

where roots of the later equation are , 1 , -1 , sqrt(2), -sqrt(2)

[shi-ting ka]

thanks