MathDB

Lithuanian TST 2014 #3

Source:

April 20, 2014

linear algebramatrixquadraticsalgebrasystem of equationsalgebra solved

Problem Statement

Given such positive real numbers

a, b

and

c

, that the system of equations:

\{\begin{matrix}a^2x+b^2y+c^2z=1&&\\xy+yz+zx=1&&\end{matrix}

has exactly one solution of real numbers

(x, y, z)

. Prove, that there is a triangle, which borders lengths are equal to

a, b

and

c