Question

Решить систему: ху=350 (х-5)(у+10)=480

Answer 1

$\left \{ {{xy=350} \atop {xy+10x-5y-50=480}} \right.$
350+10x-5y-50=480
10x-5y=180
5y=10x-180      │:5
y= 2x-36
2x-36= $\frac{350}{x}$    │∙x
2$x^{2}$-36x=350   │:2
$x^{2}$-18x-175=0
D= 324-4∙(-175) = 324 + 700 = 1024
$\sqrt{D}=32$
$x_{1}= \frac{18+32}{2}= \frac{50}{2} =25$
$x_{2} = \frac{18-32}{2} = -\frac{14}{2} = -7$
$y_{1} = \frac{350}{25}= \frac{70}{5}= 14$
$y_{2} = - \frac{350}{7} = - \frac{50}{1} = -50$