Question

2 xy+y= 5;
2ху+х= 6;​

Answer 1

Ответ:

$(-1,5; -2,5) \quad ; \quad (2; 1) \quad ;$

Объяснение:

ОДЗ:

$x \neq 0, \quad y \neq 0;$

Решение:

$\displaystyle \left \{ {{2xy+y=5} \atop {2xy+x=6}} \right. \bigg | - \Leftrightarrow \left \{ {{2xy-2xy+y-x=5-6} \atop {2xy+x=6}} \right. \Leftrightarrow \left \{ {{y-x=-1} \atop {2xy+x=6}} \right. \Leftrightarrow$

$\displaystyle \Leftrightarrow \left \{ {{x=y+1} \atop {2y(y+1)+y+1=6}} \right. \Leftrightarrow \left \{ {{x=y+1} \atop {2y^{2}+2y+y+1-6=0}} \right. \Leftrightarrow \left \{ {{x=y+1} \atop {2y^{2}+3y-5=0}} \right. \Leftrightarrow$

$\displaystyle \Leftrightarrow \left \{ {{x=y+1} \atop {2y^{2}+5y-2y-5=0}} \right. \Leftrightarrow \left \{ {{x=y+1} \atop {y(2y+5)-1(2y+5)=0}} \right. \Leftrightarrow$

$\displaystyle \Leftrightarrow \left \{ {{x=y+1} \atop {(y-1)(2y+5)=0}} \right. \Leftrightarrow \left \{ {{x=y+1} \atop {y-1=0}} \right. \vee \left \{ {{x=y+1} \atop {2y+5=0}} \right. \Leftrightarrow \left \{ {{x=2} \atop {y=1}} \right. \vee \left \{ {{x=-1,5} \atop {y=-2,5}} \right. ;$

$(-1,5; -2,5) \quad ; \quad (2; 1) \quad ;$