Question

решите пожаааалуййста

Answer 1

$left { {{x+y=72} atop {sqrt[3]{x}+sqrt[3]{y}=6}} right. ; left { {{(sqrt[3]{x}+sqrt[3]{y})(sqrt[3]{x^2}-sqrt[3]{xy}+sqrt[3]{y})=72} atop {sqrt[3]{x}+sqrt[3]{y}=6}} right. ; ; Rightarrow \\1)quad sqrt[3]{x^2}-sqrt[3]{xy}+sqrt[3]{y^2}=72:6; \\ (sqrt[3]{x^2}+sqrt[3]{y^2})-sqrt[3]{xy}=12$

$sqrt[3]{x^2}+sqrt[3]{y^2}=12+sqrt[3]{xy}$

$2)quad 6^2=(sqrt[3]{x}+sqrt[3]{y})^2=sqrt[3]{x^2}+sqrt[3]{y^2}+2sqrt[3]{xy}\\sqrt[3]{x^2}+sqrt[3]{y^2}=36-2sqrt[3]{xy}$

$3)12+sqrt[3]{xy}=36-2sqrt[3]{xy}$

$3sqrt[3]{xy}=24\\sqrt[3]{xy}=8; ; to ; ; xy=8^3; ,; xy=512\\4) quad left { {{x+y=72} atop {xy=512}} right. ; left { {{y=72-x} atop {x(72-x)=512}} right. ; left { {{y=72-x} atop {x^2-72x+512=0}} right. ; left { {{y_1=64,; y_2=8} atop {x_1=8,; x_2=64}} right. \\Otvet:quad (8,64); ;; (64,8); .$