Question

Решите систему уравнений! Срочно!
$left { {{ sqrt{xy} * ( sqrt{x} + sqrt{y} )=6} atop {( sqrt{x} + sqrt{y} ) (x- sqrt{xy} +y)=9} right.$

Answer 1

$left { {{sqrt{xy}cdot (sqrt{x}+sqrt{y})=6} atop {(sqrt{x}+sqrt{y})(x-sqrt{xy}+y)=9}} right. ; ,; ; u=sqrt{x}+sqrt{y}; ,; ; v= sqrt{xy}\\ODZ:; ; xgeq 0; ,; ygeq 0\\x+y=(sqrt{x}-sqrt{y})^2-2sqrt{xy}\\ left { {{uv=6} atop {u(u^2-3v)=9}} right. ; left { {{v=frac{6}{u}} atop {u(u^2-3cdot frac{6}{u})=9}} right. ; left { {{v=frac{6}{u}} atop {u^3=27}} right. ; left { {{v=2} atop {u=3}} right. ; left { {{sqrt{xy}=2} atop {sqrt{x}+sqrt{y}=3}} right. \\t=sqrt{x}; ,; p=sqrt{y}$

$left { {{tp=2} atop {t+p=3}} right. ; left { {{t(3-t)=2} atop {p=3-t}} right. ; left { {{t^2-3t+2=0} atop {p=3-t}} right.; left { {{t_1=1; ,; t_2=2} atop {p_1=2; ,; p_2=1}} right. \\ left { {{ sqrt{x}=1} atop { sqrt{y}=2}} right. ; ; ; ili; ; ; left { {{sqrt{x}=2} atop {sqrt{y}=1}} right. \\left { {{x=1} atop {y=4}} right. ; ; ; ili; ; ; left { {{x=4} atop {y=1}} right.\\Otvet:; ; (1,4); ,; (4,1); .$