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f(x)=x^2-6x+5, f(y)<=f(x)<= - f(y) (II Soros Olympiad 1995-96 R3 9.4)

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June 4, 2024
system of equationsinequalitiesalgebraanalytic geometry

Problem Statement

Let f(x)=x2−6x+5f(x)=x^2-6x+5. On the plane (x,y)(x, y) draw a set of points M(x,y)M(x, y) whose coordinates satisfy the inequalities {f(x)+f(y)≤0f(x)−f(y)≥0\begin{cases} f(x)+f(y)\le 0 \\ f(x)-f(y)\ge 0 \end{cases}
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