0\; \; \to \; \; y>x\; ,\; \; \; 6>2\; (!)\\\\Otvet:\; \; (2,6)\; ." alt="\left \{ {3^{x}\cdot 2^{y}=576} \atop {log_{\sqrt2}(y-x)=4}} \right. \; \left \{ {{3^{x}\cdot 2^{y}=576} \atop {y-x=(\sqrt2)^4}} \right. \; \; \left \{ {{3^{x}\cdot 2^{y}=576} \atop {y-x=2^2}} \right. \; \; \left \{ {{3^{x}\cdot 2^{x+4}=576} \atop {y=x+4}} \right. \\\\3^{x}\cdot 2^{x+4}=576\\\\3^{x}\cdot 2^{x}\cdot 2^4=576\; ,\; \; (3\cdot 2)^{x}\cdot 16=576\; ,\; \; 6^{x}\cdot 16=576\; ,\\\\6^{x}=36\; ,\; \; 6^{x}=6^2\; \; \Rightarrow \; \; \boxed{x=2}\\\\y=x+4=2+4=6\; ,\; \; \boxed {y=6}\\\\ODZ:\; \; y-x>0\; \; \to \; \; y>x\; ,\; \; \; 6>2\; (!)\\\\Otvet:\; \; (2,6)\; ." align="absmiddle" class="latex-formula">