[tex]\displaystyle\bf\\\left \{ {{x^{2} - y^{2} =5} \atop {x^{4}- y^{4} =65}} \right. \\\\\\:\left \{ {{(x^{2} -y^{2})\cdot(x^{2} +y^{2} )=65 } \atop {x^{2} -y^{2}=5 }} \right. \\--------------\\x^{2} +y^{2} =13\\\\\\Otvet: \ x^{2} +y^{2} =13[/tex]

Система имеет четыре решения : ( - 3 ; - 2) , ( - 3 ; 2) , (3 ; - 2) , ( 3 ; 2) .