why can matlab NOT solve this simple equation (2015a version) ?

>> syms x;
>> solve(2*x-1==0)
ans =
1/2
>> solve(5000*(1/x - 1/(x*(1+x)^15)) - 35000 == 0)

>> solve(5000*(1/x - 1/(x*(1+x)^15)) - 35000 == 0, 'real', true)

There is a solution: 0.114913

what is wrong here?

Answer 1

[Star Strider]

Nothing is wrong. Your equation has 15 solutions, only one of which is real.

Use vpasolve, and to get the one real solution, select it as having no imaginary component:

x1 = vpasolve(5000*(1/x - 1/(x*(1+x)^15)) - 35000 == 0);
real_x1 = x1(imag(x1)==0)

real_x1 =

0.11491336334766181651570218695387

Answer 2

[Walter Roberson]

Notice the warning messages about parameterized solutions and ReturnConditions. Then it warns you that the answer that follows is subject to a particular condition.

The way to interpret what you received is that solve() is replying that "all x that meet a particular condition are solutions, and if you were to request that the conditions be output you could capture the condition for further manipulation"

If you wanted the numeric value you could vpa() or double() the result. There is no nice closed-form solution for the result. 15 degree polynomials seldom have nice closed-form solutions.