MathDB

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Problems(1)

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

Source:

9/20/2010
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.
trigonometryalgebrasystem of equationstrigonometric substitutionIMO Shortlist