Let $x,y \in (0,1)$, and suppose that $$ x^2-2x+y^2<0. $$
How to prove that $$ -x^3-xy^2+4y^2 \ge 0. $$ holds?
The motivation comes from a certain geometric problem (a bit long to describe here).
2026-03-27 21:23:30.1774646610
Proving a conditional algebraic inequality
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The statement is not true because $(x,y) = (0.1, 0.01)$ satisfies the first inequality but not the second one.