[color=#999999]This activity belongs to the [i]GeoGebra book[/i] [url=https://www.geogebra.org/m/sw2cat9w]GeoGebra Principia[/url].[/color][br][br][br]However, not always does the algebraic equation allow GeoGebra to represent the corresponding inequations. As shown in the official manual [url=https://wiki.geogebra.org/en/Inequalities][img]https://www.geogebra.org/resource/scjbyz2p/0tuzuVw455vxurEw/material-scjbyz2p.png[/img][/url], this representation is limited to the following cases:  [br][list][*]Polynomial inequalities in one variable, like x³ > x + 1 [br][/*][*][b]Quadratic [/b]inequalities in two variables, like x² + y² + x y < 4[br][/*][*]Linear inequalities in one of the variables, like 2x > sen(y) or y < sqrt(x).[br][/*][/list]When we find the algebraic equation corresponding to XA – XB = k, we obtain the same as the one corresponding to XA + XB = k:  [br][br] [color=#CC3300]4 XB2 XA2 = (k² – XA2 – XB2)² [/color][br]  [br]This equation reduces to a quadratic in two variables, allowing GeoGebra to represent its corresponding inequations.[br][list][*][color=#808080]Note: The common quadratic equation of the ellipse and hyperbola is nothing but the general equation of a conic [b]a x² + b x y + c y² + d x + e y + f = 0[/b], where the ellipse and the hyperbola differ only by the sign of the discriminant[b] b² – 4 a c.[/b][/color][br][/*][/list]However, the algebraic equation corresponding to XA XB = k doesn't represent a conic, so GeoGebra can't represent the corresponding inequations. On the other hand, the algebraic equation corresponding to XA = k XB becomes a conic once again, allowing GeoGebra to represent the corresponding inequations.

[color=#999999]Author of the construction of GeoGebra: [url=https://www.geogebra.org/u/rafael]Rafael Losada[/url].[/color]