Question

система уравнений y=6/x y=5+x помогите решить

Answer 1

Ответ:

$(-6 ;-1) \quad ; \quad (1; 6) \quad ;$

Пошаговое объяснение:

ОДЗ:

$x \neq 0;$

Решение:

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

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

$\displaystyle \left \{ {{y=\dfrac{6}{x}} \atop {x+6=0}} \right. \vee \left \{ {{y=\dfrac{6}{x}} \atop {x-1=0}} \right. \Leftrightarrow \left \{ {{y=\dfrac{6}{x}} \atop {x=-6}} \right. \vee \left \{ {{y=\dfrac{6}{x}} \atop {x=1}} \right. \Leftrightarrow \left \{ {{x=-6} \atop {y=-1}} \right. \vee \left \{ {{x=1} \atop {y=6}} \right. ;$

$(-6 ;-1) \quad ; \quad (1; 6) \quad ;$