Question

решить систему уравнений

Answer 1

$\displaystyle\bf\\\left \{ {{\sqrt[4]{x+y} -\sqrt[4]{x-y} =2} \atop {\sqrt{x+y} -\sqrt{x-y} =8}} \right. \\\\\\\sqrt[4]{x+y} =m \ \ \ \Rightarrow \ \ \ \sqrt{x+y} =m^{2} \\\\\\\sqrt[4]{x-y} =n \ \ \ \Rightarrow \ \ \ \sqrt{x-y} =n^{2} \\\\\\\left \{ {{m-n=2} \atop {m^{2} - n^{2} =8}} \right. \\\\\\\left \{ {{m-n=2} \atop {(m-n)(m+n)=8}} \right. \\\\\\\left \{ {{m-n=2} \atop {2\cdot(m+n)=8}} \right. \\\\\\+\left \{ {{m-n=2} \atop {m+n=4}} \right. \\--------\\2m=6\\\\m=3$

$\displaystyle\bf\\n=4-m=4-3=1\\\\\\\left \{ {{\sqrt[4]{x+y} =3} \atop {\sqrt[4]{x-y} =1}} \right. \\\\\\\left \{ {{\Big(\sqrt[4]{x+y} \Big)^{4} =3^{4} } \atop {\Big(\sqrt[4]{x-y} \Big)^{4} =1^{4} }} \right. \\\\\\+\left \{ {{x+y=81} \atop {x-y=1}} \right. \\--------\\2x=82\\\\x=41\\\\y=81-x=81-41=40\\\\Otvet \ : \ \Big(41 \ ; \ 40\Big)$

Answer 2

Відповідь: (41;40)

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