Потому что любая степень со знаком "минус" - переворачивает число.
То есть если будет 5 в -1 степени, то получиться 1/5 => 5 в -2 степени = 1/25
Надеюсь нормально обьяснил
Б) выражаем x из 2 уравнения и подставляем в 1
![x=y+4 \\y+4+2y^2=4 \\2y^2+y=0 \\y(2y+1)=0 \\y_1=0 \\2y+1=0 \\2y=-1 \\y_2=-0,5 \\x_1=0+4=4 \\x_2=-0,5+4=3,5](https://tex.z-dn.net/?f=x%3Dy%2B4%0A%5C%5Cy%2B4%2B2y%5E2%3D4%0A%5C%5C2y%5E2%2By%3D0%0A%5C%5Cy%282y%2B1%29%3D0%0A%5C%5Cy_1%3D0%0A%5C%5C2y%2B1%3D0%0A%5C%5C2y%3D-1%0A%5C%5Cy_2%3D-0%2C5%0A%5C%5Cx_1%3D0%2B4%3D4%0A%5C%5Cx_2%3D-0%2C5%2B4%3D3%2C5)
Ответ: (4;0), (3,5;-0,5)
в) выражаем x из 2 уравнения и подставляем в 1
![x=5-y \\(5-y)^2+y^2=13 \\y^2-10y+25+y^2-13=0 \\2y^2-10y+12=0 \\y^2-5y+6=0 \\D=25-24=1 \\y_1= \frac{5+1}{2} =3 \\y_2= \frac{5-1}{2}=2 \\x_1=5-3=2 \\x_2=5-2=3](https://tex.z-dn.net/?f=x%3D5-y%0A%5C%5C%285-y%29%5E2%2By%5E2%3D13%0A%5C%5Cy%5E2-10y%2B25%2By%5E2-13%3D0%0A%5C%5C2y%5E2-10y%2B12%3D0%0A%5C%5Cy%5E2-5y%2B6%3D0%0A%5C%5CD%3D25-24%3D1%0A%5C%5Cy_1%3D+%5Cfrac%7B5%2B1%7D%7B2%7D+%3D3%0A%5C%5Cy_2%3D+%5Cfrac%7B5-1%7D%7B2%7D%3D2%0A%5C%5Cx_1%3D5-3%3D2%0A%5C%5Cx_2%3D5-2%3D3+)
Ответ: (2;3), (3;2)
г) выражаем x из 2 уравнения и подставляем в 1
![x=y+3 \\(y+3)^2+y^2=17 \\y^2+6y+9+y^2=17 \\2y^2+6y-8=0 \\y^2+3y-4=0 \\D=9+16=25=5^2 \\y_1= \frac{-3+5}{2} =1 \\y_2= \frac{-3-5}{2} =-4 \\x_1=1+3=4 \\x_2=-4+3=-1](https://tex.z-dn.net/?f=x%3Dy%2B3%0A%5C%5C%28y%2B3%29%5E2%2By%5E2%3D17%0A%5C%5Cy%5E2%2B6y%2B9%2By%5E2%3D17%0A%5C%5C2y%5E2%2B6y-8%3D0%0A%5C%5Cy%5E2%2B3y-4%3D0%0A%5C%5CD%3D9%2B16%3D25%3D5%5E2%0A%5C%5Cy_1%3D+%5Cfrac%7B-3%2B5%7D%7B2%7D+%3D1%0A%5C%5Cy_2%3D+%5Cfrac%7B-3-5%7D%7B2%7D+%3D-4%0A%5C%5Cx_1%3D1%2B3%3D4%0A%5C%5Cx_2%3D-4%2B3%3D-1)
Ответ: (4;1), (-1;-4)
д) выражаем x из 2 уравнения и подставляем в 1
![x=3-y \\(3-y)^2-3y+9=0 \\y^2-6y+9-3y+9=0 \\y^2-9y+18=0 \\D=81-72=9=3^2 \\y_1= \frac{9+3}{2} =6 \\y_2= \frac{9-3}{2} =3 \\x_1=3-6=-3 \\x_2=3-3=0](https://tex.z-dn.net/?f=x%3D3-y%0A%5C%5C%283-y%29%5E2-3y%2B9%3D0%0A%5C%5Cy%5E2-6y%2B9-3y%2B9%3D0%0A%5C%5Cy%5E2-9y%2B18%3D0%0A%5C%5CD%3D81-72%3D9%3D3%5E2%0A%5C%5Cy_1%3D+%5Cfrac%7B9%2B3%7D%7B2%7D+%3D6%0A%5C%5Cy_2%3D+%5Cfrac%7B9-3%7D%7B2%7D+%3D3%0A%5C%5Cx_1%3D3-6%3D-3%0A%5C%5Cx_2%3D3-3%3D0)
Ответ: (-3;6), (0;3)
е) выражаем x из 2 уравнения и подставляем в 1
![x=2-y \\(2-y)^2+4y-8=0 \\y^2-4y+4+4y-8=0 \\y^2-4=0 \\(y-2)(y+2)=0 \\y_1=2 \\y_2=-2 \\x_1=2-2=0 \\x_2=2+2=4 ](https://tex.z-dn.net/?f=x%3D2-y%0A%5C%5C%282-y%29%5E2%2B4y-8%3D0%0A%5C%5Cy%5E2-4y%2B4%2B4y-8%3D0%0A%5C%5Cy%5E2-4%3D0%0A%5C%5C%28y-2%29%28y%2B2%29%3D0%0A%5C%5Cy_1%3D2%0A%5C%5Cy_2%3D-2%0A%5C%5Cx_1%3D2-2%3D0%0A%5C%5Cx_2%3D2%2B2%3D4%0A)
Ответ: (0;2), (4;-2)
ж) выражаем x из 2 уравнения и подставляем в 1
![x= \frac{12}{y} \\ \frac{12}{y} -y=1 \\-y^2-y+12=0 \\y^2+y-12=0 \\D=1+48=49=7^2 \\y_1= \frac{-1+7}{2} =3 \\y_2= \frac{-1-7}{2} =-4 \\x_1= \frac{12}{3} =4 \\x_2= \frac{12}{-4} =-3](https://tex.z-dn.net/?f=x%3D+%5Cfrac%7B12%7D%7By%7D+%0A%5C%5C+%5Cfrac%7B12%7D%7By%7D+-y%3D1%0A%5C%5C-y%5E2-y%2B12%3D0%0A%5C%5Cy%5E2%2By-12%3D0%0A%5C%5CD%3D1%2B48%3D49%3D7%5E2%0A%5C%5Cy_1%3D+%5Cfrac%7B-1%2B7%7D%7B2%7D+%3D3%0A%5C%5Cy_2%3D+%5Cfrac%7B-1-7%7D%7B2%7D+%3D-4%0A%5C%5Cx_1%3D+%5Cfrac%7B12%7D%7B3%7D+%3D4%0A%5C%5Cx_2%3D+%5Cfrac%7B12%7D%7B-4%7D+%3D-3)
Ответ: (4;3), (-3;-4)
з) выражаем x из 2 уравнения и подставляем в 1
![x= \frac{12}{y} \\ \frac{12}{y} -2y=2 \\ \frac{6}{y} -y=1 \\-y^2-y+6=0 \\y^2+y-6=0 \\D=1+24=25=5^2 \\y_1= \frac{-1+5}{2} =2 \\y_2= \frac{-1-5}{2} =-3 \\x_1= \frac{12}{2} =6 \\x_2= \frac{12}{-3} =-4](https://tex.z-dn.net/?f=x%3D+%5Cfrac%7B12%7D%7By%7D+%0A%5C%5C+%5Cfrac%7B12%7D%7By%7D+-2y%3D2%0A%5C%5C+%5Cfrac%7B6%7D%7By%7D+-y%3D1%0A%5C%5C-y%5E2-y%2B6%3D0%0A%5C%5Cy%5E2%2By-6%3D0%0A%5C%5CD%3D1%2B24%3D25%3D5%5E2%0A%5C%5Cy_1%3D+%5Cfrac%7B-1%2B5%7D%7B2%7D+%3D2%0A%5C%5Cy_2%3D+%5Cfrac%7B-1-5%7D%7B2%7D+%3D-3%0A%5C%5Cx_1%3D+%5Cfrac%7B12%7D%7B2%7D+%3D6%0A%5C%5Cx_2%3D+%5Cfrac%7B12%7D%7B-3%7D+%3D-4)
Ответ: (6;2), (-4;-3)
<em>Решение:</em>
<em>a₁=8;</em>
<em>a₂=a₁+d;</em>
<em>6,5=8+d;</em>
<em>d=-1,5;</em>
<em>a₇=a₁+6d;</em>
<em>a₇=8+6*(-1,5)=8-9=-1;</em>
<em>Ответ:a₇=-1.</em>
n - первое число, второе - следующее чётное - n+2, третье -n+4, четвёртое - n+6.