Question

решить систему :
360/y - 360/x = 2
360/y+30 - 360/x+30 = 1

Answer 1

$frac{360}{y}-frac{360}{x}=2\ frac{360}{y+30}-frac{360}{x+30}=1\\ frac{360x-360y}{xy}=2\ frac{360(x+30)- 360(y+30)}{(y+30)(x+30)}=1\ \ frac{360x-360y}{yx+30y+30x+900}=1\ frac{360x-360y}{xy}=2\\ \ 360x-360y=yx+30(y+x)+900\ 360x -360y=2yx\ \ yx+30(y+x)+900=2yx\ 30(y+x)+900=yx 30y+30x+900=yx\ 30y-yx=-30x-900\ y(30-x)=-30x-900\ y=frac{-30x-900}{30-x}\ y=frac{-30x-900}{30-x}\ frac{360(30-x)}{-30x-900}-frac{360}{x}=2\ x^2-78x-1080=0\ D=sqrt{10404}\ x_{1}=90\ x_{2}=-12$
$y_{1}=-12frac{6}{7}\ y_{2}=60$