how to solve equation like this

syms x

solx =zeros(2,4);

equation = (x^2)*(x^(1/2)+x^(1/3))-100==0;

solve(equation,x)

result => ans =

z2^6

i want solve this eqaution please

Answer 1

[Roger Stafford]

Define z = x^(1/6). Then your equation becomes:

   z^15 + z^2 - 100 = 0

You can solve this numerically using the ‘roots’ function. From those roots for z you can then easily determine the corresponding values of x, using x = z^6.

Answer 2

[Walter Roberson]

sol = solve(equation, x, 'returnconditions', true);
aux_var_name = sol.parameters;
aux_var_values = solve(sol.conditions);
all_sols = subs(sol.x, aux_var_name, aux_var_values);

The result will be something like

root(z^15 + z^14 - 100, z, 1)^6
root(z^15 + z^14 - 100, z, 14)^6
root(z^15 + z^14 - 100, z, 15)^6

Here, root(z^15 + z^14 - 100, z, 1) stands for the "first" value that satisfies z^15 + z^14 - 100 == 0 -- one of the roots of the 15 degree polynomial.

The root() stands in for the exact solution. However, you will not be able to calculate a closed form representation of that root as algebraic numbers. You can see numeric approximations using vpa(all_sols) or double(all_sols)

One of the three solutions is real valued, and the other two are complex. You might want to consider using

syms x real

if you are only interested in the real root.