MathDB

3

Part of 2004 Austrian-Polish Competition

Problems(1)

Austria-Poland 2004 system of equations

Source: Austria-Poland 2004, single competition, problem 3

2/15/2005
Solve the following system of equations in R\mathbb{R} where all square roots are non-negative: a−1−b2+1−c2=db−1−c2+1−d2=ac−1−d2+1−a2=bd−1−a2+1−b2=c \begin{matrix} a - \sqrt{1-b^2} + \sqrt{1-c^2} = d \\ b - \sqrt{1-c^2} + \sqrt{1-d^2} = a \\ c - \sqrt{1-d^2} + \sqrt{1-a^2} = b \\ d - \sqrt{1-a^2} + \sqrt{1-b^2} = c \\ \end{matrix}
linear algebramatrixtrigonometryalgebrasystem of equationsalgebra unsolved