Question

Решить систему иррациональных уравнений

Answer 1

$\left \{ {{\sqrt[3]{x}*\sqrt{y}=-8} \atop {\sqrt[3]{x}+\sqrt{y}}=7} \right. \\y\geq 0\\\sqrt[3]{x}=a\\\sqrt{y}=b,b\geq 0\\\left \{ {{ab=-8} \atop {a+b=7}} \right.\left \{ {{ab=-8} \atop {a=7-b}} \right. =(7-b)b=-8b^2-7b-8=0\\b=-1=a=8\\b=8=a=-1\\\left \{ {{\sqrt[3]{x}=-1} \atop {\sqrt{y}=8}} \right. =(x;y)=(-1;64)$