MathDB

2-variable inequality

Source: St. Petersburg 2023 9.1

August 12, 2023

inequalities

Problem Statement

Let

a, b>1

be reals such that

a+\frac{1}{a^2} \geq 5b-\frac{3}{b^2}

. Show that

a>5b-\frac{4}{b^2}