Срочно !!!100балов решите пожалуйста

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Срочно !!!100балов решите пожалуйста


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Алгебра (171 баллов) | 41 просмотров
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3,4,5

Дан 1 ответ
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1)
\left \{ {{x+y=3} \atop {x^2+y^2=29}} \right.
\left \{ {{x=3-y} \atop {x^2+y^2=29}} \right.
\left \{ {{x=3-y} \atop {(3-y)^2+y^2=29}} \right.
\left \{ {{x=3-y} \atop {9-6y+y^2+y^2=29}} \right.
\left \{ {{x=3-y} \atop {2y^2-6y-20=0}} \right.
\left \{ {{x=3-y} \atop {y^2-3y-10=0}} \right.
\left \{ {{x=3-y} \atop {(y-5)(y+2)=0}} \right.
\left \{ {{x_1=3-5=-2} \atop {y_1=5}} \right.
\left \{ {{x_2=3+2=5} \atop {y_2=-2}} \right.

2)
\left \{ {{xy=12} \atop {2(x+y)=14}} \right.
\left \{ {{xy=12} \atop {x+y=7}} \right.
\left \{ {{xy=12} \atop {x=7-y}} \right.
\left \{ {{(7-y)y=12} \atop {x=7-y}} \right.
\left \{ {{-y^2+7y-12=0} \atop {x=7-y}} \right.
\left \{ {{y^2-7y+12=0} \atop {x=7-y}} \right.
\left \{ {{(y-3)(y-4)=0} \atop {x=7-y}} \right.
\left \{ {{y_1=3} \atop {x_1=7-3=4}} \right.
\left \{ {{y_2=4} \atop {x_2=7-4=3}} \right.
Стороны прямоугольника равны 3 и 4 дм.

3)
графическое решение в прилагаемом файле
решение системы есть 4 точки: (3,4); (4,3); (-3,-4); (-4,-3)

4)
\left \{ {x^2+y^2=1} \atop {x+y=-1}} \right.
\left \{ {x^2+y^2=1} \atop {x=-y-1}} \right.
\left \{ {(-y-1)^2+y^2=1} \atop {x=-y-1}} \right.
\left \{ {y^2+2y+1+y^2=1} \atop {x=-y-1}} \right.
\left \{ {2y^2+2y=0} \atop {x=-y-1}} \right.
\left \{ {2y(y+1)=0} \atop {x=-y-1}} \right.
\left \{ {y_1=0} \atop {x_1=0-1=-1}} \right.
\left \{ {y_2=-1} \atop {x_2=1-1=0}} \right.
Решение: точки (-1,0) и (0,-1)

5)
\left \{ {{x+2y=7} \atop {xy+2y^2=14}} \right.
\left \{ {{x=7-2y} \atop {xy+2y^2=14}} \right.
\left \{ {{x=7-2y} \atop {(7-2y)y+2y^2=14}} \right.
\left \{ {{x=7-2y} \atop {7y-2y^2+2y^2=14}} \right.
imageop {7y=14}} \right. " alt=" \left \{ {{x=7-2y} \atop {7y=14}} \right. " align="absmiddle" class="latex-formula">
\left \{ {{x=7-2*2=3} \atop {y=2}} \right.


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там в 5 номере предпоследняя система равна {x=7-2y; {7y=14