Question

помогите решить надо решить систему уровнений

Answer 1

Ответ: x=125,    y=16.

Объяснение:

$\displaystyle\\\left \{ {{\sqrt[3]{x}-\sqrt[4]{y}=3 } \atop {\sqrt[4]{y}*\sqrt[3]{x}=10 }} \right. .$

Пусть ³√x=t,     ⁴√y=v≥0.      ⇒

$\displaystyle\\\left \{ {{t-v=3} \atop {t*v=10}} \right.\ \ \ \ \ \ \left \{ {t=3+v} \atop {(3+v)*v=10}} \right. \ \ \ \ \ \ \left \{ {{t=v+3} \atop {3v+v^2-10=0}} \right.\ \ \ \ \ \ \left \{ {{t=v+3} \atop {v^2+3v-10=0}} \right. \\\\\\\left \{ {{t=v+3} \atop {v^2+5v-2v-10=0\ \ \ \ \ \ }} \right. \ \ \ \ \ \ \left \{ {{t=v+3} \atop {v*(v+5)-2*(v+5)=0}} \right. \\\\\\\left \{ {{t=v+3} \atop {(v+5)*(v-2)=0}} \right. \ \ \ \ \ \ \left \{ {{t=5} \atop {v_1=-5\notin, \ \ v_2=2}} \right. .$

$\displaystyle\\\sqrt[3]{x}=5 \\\\(\sqrt[3]{x})^3=5^3 \\\\x=125.\\\\\sqrt[4]{y}=2\\\\(\sqrt[4]{y})^4=2^4\\\\y=16.$