Prove that for all positive real numbers $x, y$ holds the inequality $$x^4 + y^3 + x^2 + y + \frac{293}{500} > \frac92 xy $$ parmenides51 wrote: Prove that for all positive real numbers $x, y$ holds the inequality $$x^4 + y^3 + x^2 + y + 1 > \frac92 xy.$$