A non-linear (!) system of equations with a parameter
Source: Germany 2022, Problem 1
June 25, 2022
algebrasystem of equationsalgebra proposedquadratic equationparameterization
Problem Statement
Determine all real numbers for which the system of equations
\begin{align*}
3x^2+2y^2+2z^2&=a\\
4x^2+4y^2+5z^2&=1-a
\end{align*}
has at least one solution in the real numbers.