Question

Помогите решить систему уравнений

Answer 1

$\left \{ {{(x+0,2)^{2} +(y+0,3)^{2}=1} \atop {x+y=0,9}} \right.\\\\\left \{ {{(x+0,2)^{2} +(y+0,3)^{2}=1} \atop {(x+0,2)+(y+0,3)=1,4}} \right.\\\\x+0,2=m\\y+0,3=n\\\\\left \{ {{m^{2}+n^{2}=1} \atop {m+n=1,4}} \right.\\\\\left \{ {{(m+n)^{2}-2mn=1} \atop {m+n=1,4}} \right.$

$\left \{ {{1,4^{2} -2mn=1} \atop {m+n=1,4}} \right.\\\\\left \{ {{2mn=0,96} \atop {m+n=1,4}} \right.\\\\\left \{ {{m*n=0,48} \atop {m+n=1,4}} \right.\\\\1)\left \{ {{m=0,6} \atop {n=0,8}} \right.\\\\\left \{ {{x+0,2=0,6} \atop {y+0,3=0,8}} \right.\\\\\left \{ {{x_{1}=0,4 } \atop {y_{1}=0,5 }} \right.$

$2)\left \{ {{m=0,8} \atop {n=0,6}} \right.\\\\\left \{ {{x+0,2=0,8} \atop {y+0,3=0,6}} \right.\\\\\left \{ {{x_{2}=0,6 } \atop {y_{2}=0,3 }} \right.\\\\Otvet:(0,4;0,5),(0,6;0,3)$

$\left \{ {{x-y=1} \atop {x^{3}-y^{3}=7}} \right.\\\\:\left \{ {{(x-y)(x^{2}+xy+y^{2})=7} \atop {x-y=1}} \right.\\---------\\x^{2}+xy+y^{2}=7\\\\\left \{ {{x=1+y} \atop {x^{2}+xy+y^{2}=7}} \right.\\\\\left \{ {{x=y+1} \atop {(y+1)^{2}+y(y+1)+y^{2}=7}} \right.\\\\\left \{ {{x=y+1} \atop {y^{2}+2y+1+y^{2}+y+y^{2}=7}} \right.\\\\\left \{ {{3y^{2}+3y-6=0} \atop {x=y+1}} \right.\\\\\left \{ {{y^{2}+y-2=0} \atop {x=y+1}} \right.$

$1)\left \{ {{y_{1}=-2 } \atop {x=-2+1}} \right.\\\\\left \{ {{y_{1} =-2} \atop {x_{1} =-1}} \right.\\\\2)\left \{ {{y_{2}=1 } \atop {x_{2} =1+1}} \right.\\\\\left \{ {{y_{2}=1 } \atop {x_{2}=2 }} \right.\\\\Otvet:(-1;-2),(2;1)$

$\left \{ {{x^{-1} +y^{-1}=5} \atop {x^{-2}+y^{-2}=13}} \right.\\\\x^{-1}=m\Rightarrow x^{-2}=m^{2}\\y^{-1}=n\Rightarrow y^{-2}=n^{2}\\\\\left \{ {{m+n=5} \atop {m^{2} +n^{2}=13 }} \right.\\\\-\left \{ {{m^{2}+2mn+n^{2}=25} \atop {m^{2}+n^{2}=13}} \right.\\---------\\2mn=12\\m*n=6\\\\\left \{ {{m+n=5} \atop {m*n=6}} \right.\\\\1)\left \{ {{m=2} \atop {n=3}} \right. \\\\\left \{ {{x^{-1}=2 } \atop {y^{-1}=3 }} \right.\\\\\left \{ {{x=\frac{1}{2} } \atop {y=\frac{1}{3}}} \right.$

$2)\left \{ {{m=3} \atop {n=2}} \right.\\\\\left \{ {{x^{-1}=3} \atop {y^{-1} =2}} \right.\\\\\left \{ {{x_{2}=\frac{1}{3}} \atop {y_{2}=\frac{1}{2}}} \right.\\\\Otvet:(\frac{1}{2};\frac{1}{3}),(\frac{1}{3};\frac{1}{2})$