MathDB

4x4 system, symmetry, a^2 = (\sqrt{bc}\sqrt[3]{bcd})/(b+c)(b+c+d)

Source: Austrian Federal Competition For Advanced Students 2004, Part 2, p5

August 30, 2019

algebrasystem of equations

Problem Statement

Solve the following system of equations in real numbers:

\begin{cases} a^2 = \cfrac{\sqrt{bc}\sqrt[3]{bcd}}{(b+c)(b+c+d)} \\ b^2 =\cfrac{\sqrt{cd}\sqrt[3]{cda}}{(c+d)(c+d+a)} \\ c^2 =\cfrac{\sqrt{da}\sqrt[3]{dab}}{(d+a)(d+a+b)} \\ d^2 =\cfrac{\sqrt{ab}\sqrt[3]{abc}}{(a+b)(a+b+c)} \end{cases}