MathDB

10.1

Part of 2001 Saint Petersburg Mathematical Olympiad

Problems(1)

Inequality on quadratic trinomials

Source: St. Petersburg MO 2001, 10th grade, P1

4/24/2023
Quadratic trinomials ff and gg with integer coefficients obtain only positive values and the inequality f(x)g(x)≥2\dfrac{f(x)}{g(x)}\geq \sqrt{2} is true ∀x∈R\forall x\in\mathbb{R}. Prove that f(x)g(x)>2\dfrac{f(x)}{g(x)}>\sqrt{2} is true ∀x∈R\forall x\in\mathbb{R}
[I]Proposed by A. Khrabrov
inequalitiesquadraticsquadratic trinomialalgebra