MathDB
Determine a,b,c such that system of equations is compatible

Source:

September 20, 2010
trigonometryalgebrasystem of equationstrigonometric substitutionIMO Shortlist

Problem Statement

Determine all the triples (a,b,c)(a, b, c) of positive real numbers such that the system ax+by−cz=0,ax + by -cz = 0,a1−x2+b1−y2−c1−z2=0,a \sqrt{1-x^2}+b \sqrt{1-y^2}-c \sqrt{1-z^2}=0, is compatible in the set of real numbers, and then find all its real solutions.
Back to ProblemsView on AoPS