Question

Помогите пожалуйста решить систему

Answer 1

$\left \{ {{4^{1+log_{4}(x^{2}+y^{2})}=20} \atop {log_{\sqrt{3}}(x^{2}-y^{2})-2=0 }} \right.\\\\\\\left \{ {{4*4^{log_{4}(x^{2}+y^{2})}=20 \atop {log_{\sqrt{3}}(x^{2}-y^{2})=2}} \right.\\\\\\+\left \{ {{x^{2}+y^{2}=5} \atop {x^{2}-y^{2}=3}} \right.\\ ------\\2x^{2}=8\\\\x^{2}=4\\\\x_{1}=-2\\\\x_{2}=2\\\\y^{2}=5-x^{2}=5-4=1\\\\y_{1} =-1\\\\y_{2}=1\\\\ODZ:\\\\1)x^{2}+y^{2}=4+1=5>0\\\\2)x^{2}-y^{2}=4-1=3>0\\\\Otvet:\boxed{(-2;-1),(-2;1),(2;-1),(2;1)}$