Let $x$ and $y$ be positive real numbers with $(x-1)(y-1)\ge1$. Prove that for sides $a,b,c$ of an arbitrary triangle we have $a^2x+b^2y>c^2$.
Source: Ukraine 1999 Grade 9 P2
Tags: geometric inequality, geometry, inequalities
Let $x$ and $y$ be positive real numbers with $(x-1)(y-1)\ge1$. Prove that for sides $a,b,c$ of an arbitrary triangle we have $a^2x+b^2y>c^2$.