Maximize answer of second order Polynomial inequality

Dear matlab user,

I would like to solve a second order polynomial inequality as follows:

Where I would like to maximize the value of x when a>0 ofcourse. I use the following example

syms x
ineq = 0.99*x^2-99<0;
x_num = solve(ineq, x);

The value it returns gives: x_num = 0. Which satisfies the constraint ofcourse. However I would like to find the maximum value for x (which would be 10-eps). How do I specify the maximization criteria with the solve command.

Answer 1

[David Goodmanson]

Hi Luuk

It makes more sense to find the boundaries of the inequality:

syms x
eqn1 = 0.99*x^2-99==0;
x_num = solve(eqn1, x)
if isreal(x_num)    % if the roots are complex there is no solution
  a = max(x_num)    % upper bound
end
     a = 10

Since the values that satisfy the inequality form an open set, the set has a supremum x = 10 that is not a member of the set. So there is no 'largest number' that satisfies the inequality. As a demo you can subrtact off eps or anything that seems small enough, for example

a - 1e-20
   ans = 999999999999999999999/100000000000000000000

and if that answer seems clumsy there is

vpa(a - 1e-20,25) 
   ans = 9.99999999999999999999