Răspuns:
Explicație pas cu pas:
[tex]\displaystyle\begin{cases}4\log_4(x-y)+\log_2(x+y)=6\\\sqrt{x-y}=2\end{cases}\Leftrightarrow\begin{cases}2\log_{2}(x-y)+\log_2(x+y)=6\\x-y=4\end{cases}\\\texttt{Prima relatie poate fi scrisa sub forma :}\\\log_2{[(x-y)^2(x+y)]}=6\\(x-y)^2(x+y)=64\\16\cdot(x+y)=64\\x+y=4\\\texttt{Obtinem sistemul :}\\\begin{cases}x-y=4\\x+y=4\end{cases}\\------+\\2x=8\Rightarrow x=4\\4+y=4\Rightarrow y=0\\\texttt{Solutia sistemului este }(x,y)=(4,0)[/tex]
