Try the 'ReturnConditions' option:
syms x
ineq = x^4 +7*x -3*x^3 -6 > 0;
S = solve(x^4 +7*x -3*x^3 -6 > 0, x,'IgnoreAnalyticConstraints', true, 'MaxDegree', 4, 'Real', true, 'ReturnConditions', true)
S =
struct with fields:
x: [2×1 sym]
parameters: [1×1 sym]
conditions: [2×1 sym]
Check the conditions on "x".
S.conditions
ans =
x < 1/3 - (61/54 - 29^(1/2)/6)^(1/3) - 7/(9*(61/54 - 29^(1/2)/6)^(1/3))
2 < x
Under these two conditions, the inequality is always satisfied. I think this is the union of two conditions you're looking for? For more info, see the documentation on 'ReturnConditions'.
Without 'ReturnConditions', I think "solve" is simply returning valid values of "x". But I'm not sure right now.
Best Answer