Question 181
For any non-negative real numbers $x$ and $y$ show the inequality:
$$
x^2 y^2 + x^2 y + xy^2 \leq x^4 y + x + y^4.
$$
$$
x^2 y^2 + x^2 y + xy^2 \leq x^4 y + x + y^4.
$$
MathNet 2022-part-05 — 197 problems (EN–VI) Question 181
Math Olympiad Vault · MathNet 2022-part-05 — 197 problems (EN–VI)