Confused about function solve

I am trying to use the function "solve" to find out the solution of inequality specified in cond1. Cond1 is shown in the following picture:

However, the solution is not obtained. I also plot the function given by the left of "cond1". Corresponding result shows there exactly exists the feasible solution.

Help!

Thank you in advance!

syms x;
cond1 = (x - 7) * x^2 / 2 - (4 + x)*2 >= 0;
sol = solve(cond1, x, 'ReturnConditions', true);
sol.conditions

[Walter Roberson]

Convert it to an equality and solve(), and throw away any complex-valued roots. Then for each root, check to see which side of the root the inequality holds on.

[Rik]

Comment posted as flag by yuquan xiao:

Thank you! But I still do not know why such an inequality can not be directly solved with solve().

Answer 1

[Milan Padhiyar]

Hello Yuquan,

When you are trying to find the root of an inequality equation using the ‘solve’ function, sometimes it is required to give assumptions for the variable to get an explicit solution.

For example, in your query, if we assume that ‘x’ is greater than zero then we can get an explicit solution.

Please find here the modified code:

syms x;
assume(x > 0);
cond1 = (x - 7) * x^2 / 2 - (4 + x)*2 >= 0;
sol = solve(cond1, x, 'ReturnConditions', true);
sol.conditions

Please refer to the below link for example on finding roots of an inequality equation.

https://www.mathworks.com/help/symbolic/solve.html#bue6mw_-1

Thank You!

[yuquan xiao]

Thank you very much! It works!