$\left \{ {x^{3}-y^{3}=7} \atop {x-y=1}} \right.\\\\:\left \{ {{(x-y)(x^{2}+xy+y^{2})=7} \atop {x-y=1}} \right.\\\\\left \{ {{x^{2}+xy+y^{2} =7} \atop {x-y=1}} \right.\\\\\left \{ {{x=y+1} \atop {(y+1)^{2}+y(y+1)+y^{2}=7 } \right.\\\\\left \{ {{y^{2}+2y+1+y^{2}+y+y^{2}=7} \atop {x=y+1}} \right.$

$\left \{ {{3y^{2}+3y-6=0 } \atop {x=y+1}} \right.\\\\\left \{ {{y^{2}+y-2=0} \atop {x=y+1}} \right.\\\\1)\left \{ {{y=-2} \atop {x=-2+1}} \right.\\\\\left \{ {{y=-2} \atop {x=-1}} \right.\\\\2)\left \{ {{y=1} \atop {x=1+1}} \right.\\\\\left \{ {{y=1} \atop {x=2}} \right.\\\\Otvet:(-1;-2),(2;1)$

$\frac{2Cos^{2}\alpha-1}{2Sin\alphaCos\alpha}+\frac{Sin3\alpha -Sin\alpha}{Cos3\alpha+Cos\alpha}=\frac{Cos2\alpha}{Sin2\alpha}+\frac{2Sin\frac{3\alpha-\alpha}{2}Cos\frac{3\alpha+\alpha}{2}}{2Cos\frac{3\alpha+\alpha}{2}Cos\frac{3\alpha-\alpha}{2}} =\frac{Cos2\alpha}{Sin2\alpha} +\frac{Sin\alpha Cos2\alpha}{Cos2\alpha Cos\alpha}=\frac{Cos2\alpha}{Sin2\alpha}+\frac{Sin\alpha}{Cos\alpha}=\frac{Cos2\alpha Cos\alpha+Sin2\alpha Sin\alpha}{Sin2\alpha Cos\alpha}=$

$=\frac{Cos(2\alpha-\alpha)}{Sin2\alpha Cos\alpha}=\frac{Cos\alpha}{Sin2\alpha Cos\alpha} =\frac{1}{Sin2\alpha}\\\\\frac{1}{Sin2\alpha}=\frac{1}{Sin2\alpha }$

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4 года назад