Question

1043 система. Как решить задачу

Answer 1

$left { {{ sqrt[3]{x} +sqrt[3]{y}=1 } atop {xy=-8}} right. ; left { {{( sqrt[3]{x}+ sqrt[3]{y} )^3=1^3} atop {xy=-8}} right. ; left { {{x+y+3sqrt[3]{xy}cdot (sqrt[3]{x}+sqrt[3]{y})=1} atop {x=2}} right. \\ left { {{x+y+3cdot sqrt[3]{-8}cdot 1=1} atop {xy=-8}} right. ; left { {{x+y=7} atop {xy=-8}} right. ; left { {{y=7-x} atop {x(7-x)=-8}} right.$

$-x^2+7x+8=0; ,; x^2-7x-8=0; ,; x_1=-1,; x_2=8\\ left { {{x_1=-1,; x_2=8} atop {y_1=8,; y_2=-1}} right.$

$Otvet:; ; (-1,8); ,; ; (8,-1); .$