Cos70+ 8cos20cos40cos80=2cos^2 35

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Алгебра

1 ответ:

Андрей123434 года назад

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Решить систему уравнений xy+x-y=7 x^2y-xy^2=6

Павел Палеков

$\left \{ {{xy+x-y=7} \atop {x^2y-xy^2=6}} \right.\; \left \{ {{xy+x-y=7} \atop {xy\cdot (x-y)=6}} \right.\; \; t=xy\; ,\; (x-y)=p\; \; \left \{ {{t+p=7} \atop {tp=6}} \right.\; \left \{ {{t=7-p} \atop {(7-p)\cdot p=6}} \right. \\\\\left \{ {{t=7-p} \atop {p^2-7p+6=0}} \right. \; \left \{ {{t=7-p} \atop {p_1=1\; ,\; t_2=6}} \right. \; \left \{ {{t_1=6\; ,\; t_2=1} \atop {p_1=1\; ,\; p_2=6}} \right.\; \; \to \; \; (6,1)\; ,\; (1,6)\\\\a)\; \; t_1=6\; ,\; p_1=1\\\\\left \{ {{xy=6} \atop {x-y=1}} \right.\; \left \{ {{(y+1)\cdot y=6} \atop {x=y+1}} \right.\; \left \{ {{y^2+y-6=0} \atop {x=y+1}} \right.\; \left \{ {{y_1=-3\; ,\; y_2=2} \atop {x_1=-2\; ,\; x_2=3}} \right. \; \; \to \; \; (-2,-3)\; ,\; (3,2)\\\\b)\; \; t_2=1\; ,\; p_2=6\\\\\left \{ {{xy=1} \atop {x-y=6}} \right. \; \left \{ {{(y+6)\cdot y=1} \atop {x=y+6}} \right. \; \left \{ {{y^2+6y-1=0} \atop {x=y+6}} \right. \; \left \{ {{y_1=-3-\sqrt{10}\; ,\; y_2=-3+\sqrt{10}} \atop {x_1=3-\sqrt{10}\; ,\; x_2=3+\sqrt{10}}} \right. \; \to \\\\(3-\sqrt{10},-3-\sqrt{10})\; ,\; \; (3+\sqrt{10},-3+\sqrt{10})$