How do I solve this system of equations for real number?

syms x y z

eqn1= x+y+z== 16;

eqn2= x*y+y*z+z*x ==41.75;

eqn3= x*y*z== -178;

S = solve(eqn1,x,'Real',true);

H = solve(eqn2,y,'Real',true);

F = solve(eqn3,z,'Real',true);

I want to solve for x, y, z as real numbers but idk how this is just giving me it with the other variables.

Answer 1

[Star Strider]

You have not assigned numeric values to ‘x’, ‘y’, and ‘z’, so what you currently have is the best you can do.

Answer 2

[John D'Errico]

Whats the problem? There appear to be six real solutions. Solve finds them with no problem.

xyz = solve(eqn1,eqn2,eqn3)
xyz = 
  struct with fields:

    x: [6×1 sym]
    y: [6×1 sym]
    z: [6×1 sym]
>> xyz.x
ans =
 (3*17^(1/2))/2 + 4
 4 - (3*17^(1/2))/2
 (3*17^(1/2))/2 + 4
                  8
 4 - (3*17^(1/2))/2
                  8
>> xyz.y
ans =
 4 - (3*17^(1/2))/2
 (3*17^(1/2))/2 + 4
                  8
 (3*17^(1/2))/2 + 4
                  8
 4 - (3*17^(1/2))/2
>> xyz.z
ans =
                  8
                  8
 4 - (3*17^(1/2))/2
 4 - (3*17^(1/2))/2
 (3*17^(1/2))/2 + 4
 (3*17^(1/2))/2 + 4

You can convert them to numeric form using either vpa or double.

What you cannot do is use solve as you tried to do, for some reason, thinking you could solve each equation independenty.