Question

помогите пожалуйста ​

Answer 1

Ответ:

ответ х=1 и у=625 то есть корен х равно 1 и корен у=25

Answer 2

Ответ: (625;1),  (1;625).

Объяснение:

$\displaystyle\\\left \{ {{\sqrt{x} +\sqrt{y} =26} \atop {\sqrt[4]{x} +\sqrt[4]{y}=6 }} \right. \ \ \ \ \ \\\\\\sqrt[4]{x} =t\geq 0\ \ \ \ \ \ \sqrt{x} =t^2\\\\\sqrt[4]{y}=v\geq 0\ \ \ \ \ \ \sqrt{y} =v^2\ \ \ \ \ \ \Rightarrow\\\\\left \{ {{t^2+v^2=26} \atop {t+v=6}} \right.\ \ \ \ \ \ \left \{ {{t^2+(6-t)^2=26} \atop {v=6-t}} \right. \ \ \ \ \ \ \left \{ {{t^2+36-12t+t^2=26} \atop {v=6-t}} \right.$

$\displaystyle\\\left \{ {{2t^2-12t+10=0\ |:2} \atop {v=6-t}} \right.\ \ \ \ \ \ \ \left \{ {t^2-6t+5=0} \atop {v=6-t}} \right.\ \ \ \ \ \ \left \{ {{t^2-5t-t+5=0} \atop {v=6-t}} \right. \\\\\\\left \{ {{t*(t-5)-(t-5)=0} \atop {v=6-t}} \right.\ \ \ \ \ \ \left \{ {{(t-5)*(t-1)=0} \atop {v=6-t}} \right. \ \ \ \ \ \ \left \{ {{t_1=5\ \ \ \ t_2=1} \atop {v_1=1\ \ \ \ v_2=5}} \right.$

$\displaystyle\\1)\ \left \{ {{(\sqrt[4]{x})^4 =5^4} \atop {(\sqrt[4]{y})^4=1^4 }} \right.\ \ \ \ \ \ \left \{ {{x_1=625} \atop {y_1=1}} \right. .\\\\\\2)\ \left \{ {{(\sqrt[4]{x})^4 =1^4} \atop {(\sqrt[4]{y})=5^4 }} \right. \ \ \ \ \ \ \left \{ {{x_2=1} \atop {y_2=625}} \right..$