Solving 3 equations with 3 unknowns

Hi! I am trying to see if Matlab would help me solve 3 equations with 3 unknowns. Thank you in advance!

52.11=2*[(sqrt(x*44.4)]

52.89=2*[(sqrt(x*34)+(sqrt(y*3.92)+(sqrt(z*57.4)]

46.71=2*[(sqrt(x*21.8)+(sqrt(y*25.5)+(sqrt(z*25.5)]

For the first equation, y and z=0.

Would something like this work:

syms x y z

E1 = 2*sqrt(x*44.4) == 52.11;

E2 = 2*((sqrt(x*34))+(sqrt(y*3.92))+(sqrt(z*57.4))) == 52.89;

E3 = 2*((sqrt(x*21.8))+(sqrt(y*25.5))+(sqrt(z*25.5))) == 46.71;

result = solve(E1,E2,E3);

Answer 1

[Torsten]

No problem.

A = [2*sqrt(44.4) 0 0; 2*sqrt(34) 2*sqrt(3.92) 2*sqrt(57.4);2*sqrt(21.8) 2*sqrt(25.5) 2*sqrt(25.5)];
b = [52.11;52.89;46.71];
sol = A\b

sol = 3×1

3.9102 0.7155 0.2941

x = sol(1)^2

x = 15.2897

y = sol(2)^2

y = 0.5119

z = sol(3)^2

z = 0.0865

A*sqrt([x;y;z])-b

ans = 3×1

0 0 0