Question

$left { {{ frac{x}{y} - frac{y}{x} = frac{5}{6}} atop {x+y=5}} right.$решить сиситему

Answer 1

$left { {{frac{x}{y}-frac{y}{x}=frac{5}{6}} atop {x+y=5}} right. ; left { {{frac{x^2-y^2}{xy}=frac{5}{6}} atop {x+y=5}} right. ; left { {{frac{(x-y)(x+y)}{xy}=frac{5}{6}} atop {x+y=5}} right. ; left { {{frac{5(x-y)}{xy}=frac{5}{6}} atop {x+y=5}} right. ; left { {{6(x-y)=xy} atop {y=5-x}} right. \\6(x-(5-x))=x(5-x)\\6(2x-5)=5x-x^2\\12x-30=5x-x^2\\x^2+7x-30=0\\D=169,\\x_1=frac{-7-13}{2}=-10,; x_2=3\\y_1=5-(-10)=15,; y_2=5-3=2\\Otvet:; (-10,15),; (3,2)$