Question

Решите систему уравнений ,только подробно 480/y-480/x=4 480/y+2-480/x+8=5

Answer 1

$\left \{ {{ \frac{480}{y}- \frac{480}{x} =4} \atop {\frac{480}{y+2}- \frac{480}{x+8} =5}} \right.\Rightarrow \left \{ {{ \frac{480(x-y)}{xy} =4} \atop {\frac{480(x+8)-480(y+2)}{(y+2)(x+8)} =5}} \right.\Rightarrow \left \{ { 480(x-y)=4xy} \atop {480(x+8)-480(y+2)=5(y+2)(x+8)} \right.$
$\left \{ { 120(x-y)=xy} \atop {96(x+8)-96(y+2)=(y+2)(x+8)} \right. \\ \left \{ { 120(x-y)=xy} \atop {96x+768-96y-192=xy+2x+8y+16} \right. \\ \left \{ { 120(x-y)=xy} \atop {94x-104y+560=xy} \right.$
$\left \{ { 120(x-y)=xy} \atop {94x-104y+560=120x-120y} \right. \left \{ { 120(x- \frac{13x-280}{8} )=x \frac{13x-280}{8} } \atop {y= \frac{13x-280}{8} } \right.$
Решаем первое уравнение:
$120(x- \frac{13x-280}{8} )=x \frac{13x-280}{8} \Rightarrow 120(8x-13x+280)=13 x^{2} -280x,$
13x²+320x-33600=0
D=320²-4·13·(-33600)=102400+1747200=1360²
x₁=(-320-1360)/26=-1680/26=-840/13           или      x₂=(-320+1360)/26=  1040/26=520/13=40
y₁=(13x₁-280)/8=(-840-280)/8=-140                            y₂=(13x₂-280)/8=(520-280)/8=240/8=30
ответ. (-840/13 ; - 140)   (40 ; 30)