Problem

Source: Czech-Polish-Slovak Junior Match 2014, Team p6 CPSJ

Tags: inequalities, algebra, minimum, maximum, min, max



Determine the largest and smallest fractions $F = \frac{y-x}{x+4y}$ if the real numbers $x$ and $y$ satisfy the equation $x^2y^2 + xy + 1 = 3y^2$.