Ответ(ы) на вопрос:
Гость[latex] \left \{ {{ \frac{1}{x}- \frac{1}{y}= \frac{1}{6} } \atop {xy=6}} \right. [/latex]
ОДЗ: [latex]x \neq 0,[/latex] [latex]y \neq 0[/latex]
[latex] \left \{ {{ \frac{y-x}{xy}}= \frac{1}{6} } \atop {xy=6}} \right. [/latex]
[latex] \left \{ {{{6(y-x)}{=xy}} } \atop {xy=6}} \right. [/latex]
[latex] \left \{ {{{6(y-x)}{=6}} } \atop {xy=6}} \right. [/latex]
[latex] \left \{ {y-x}{=1}} } \atop {xy=6}} \right. [/latex]
[latex] \left \{ {y}{=1+x}} } \atop {x(1+x)=6}} \right. [/latex]
[latex] \left \{ {y}{=1+x}} } \atop {x^2+x-6=0}} \right. [/latex]
[latex] x^{2} +x-6=0[/latex]
[latex]D=1^2-4*1*(-6)=25[/latex]
[latex]x_1= \frac{-1+5}{2} =2,[/latex] [latex]y_1=2+1=3[/latex]
[latex]x_2= \frac{-1-5}{2} =-3,[/latex] [latex]y_2=-3+1=-2[/latex]
Ответ: (2;3); (-3;-2)
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