2(x-7)=3
2x-14=3
2x=17
x=8,5
A26=a1+25d; a1=9; a26=44; 9+25d=44; 25d=35; d=35/25=7/5=1,4
a15=9+14*1,4=28,6; a30=9+29*1,4=40,6
S=1/2 *(28,6+40,6)*16=69,2*8=553,6
2) y17+y5=y1+16d+y1+4d=2y1+20d;
y10+y12=y1+9d+y1+11d=2y1+20d
сравнивая видим, что равенство верное!
3) a1=40; an=160
160-40=120; n=121 S=(40+160)/2 *121=12100
4)xn=x1+d(n-1) ; xn=32-2.7(n-1)
xn<0; 32-2,7(n-1)<0; -2,7(n-1)<-32; n-1>320/27;n>11целых5/27)+1; n=13
x13=32-2,7*12=32-32,4=-0,4
║ 7ху + у = 16,
║ 7ху - х = 13,
║ у*(7х + 1) = 16,
║ 7ху - х = 13,
из 1 ур-ия:
у = 16 / (7х + 1),
подставим во 2 ур-ие:
(7х * 16) / (7х + 1) - х = 13,
112х / (7х + 1) - х(7х + 1) / (7х + 1) = 13(7х + 1) / (7х + 1),
(112х - 7х² - х - 91х - 13) / (7х + 1) = 0,
(-7х² + 20х - 13) / (7х + 1) = 0,
-7х² + 20х - 13 = 0,
Д = 20² - 4*(-7)*(-13) = 400 - 364 = 36,
х1 = (-20 + 6) / (-2*7) = -14 / (-14) = 1,
х2 = (-20 - 6) / (-2*7) = -26 / (-14) = 13/7 = 1 6/7,
у1 = 16 / (7*1 + 1) = 16 / 8 = 2,
у2 = 16 / (7*1 6/7 + 1) = 16 / 14 = 8/7 = 1 1/7,
ответ: (1; 2), (1 6/7; 1 1/7)
-2x=4-x x=-4 y=8
-2x=1/3x x=0 y=0
1/3x=4-x x=3 y=1
ответ (-4,8) (0,0) (3,1)
![\left \{ {{x-2y=0} \atop {5xy+y^2=44}} \right. \left \{ {{x=2y} \atop {5xy+y^2=44}} \right.](https://tex.z-dn.net/?f=%5Cleft+%5C%7B+%7B%7Bx-2y%3D0%7D+%5Catop+%7B5xy%2By%5E2%3D44%7D%7D+%5Cright.+%5Cleft+%5C%7B+%7B%7Bx%3D2y%7D+%5Catop+%7B5xy%2By%5E2%3D44%7D%7D+%5Cright.)
Подставим первое уравнение во второе и отдельно его решим
![5(2y)y+y^2=44 \\ 10y^2+y^2=44 \\ 11y^2=44|:11 \\ y^2=4 \\ y=\sqrt{4} \\ y=+-2](https://tex.z-dn.net/?f=5%282y%29y%2By%5E2%3D44+%5C%5C+10y%5E2%2By%5E2%3D44+%5C%5C+11y%5E2%3D44%7C%3A11+%5C%5C+y%5E2%3D4+%5C%5C+y%3D%5Csqrt%7B4%7D+%5C%5C+y%3D%2B-2+)
Вернемся в систему которых теперь будет две
![1. \left \{ {{x=2y} \atop {y=2}} \right. \left \{ {{x=2*2} \atop {y=2}} \right. \left \{ {{x=4} \atop {y=2}} \right. \\2. \left \{ {{x=2y} \atop {y=-2}} \right. \left \{ {{x=2*(-2)} \atop {y=-2}} \right. \left \{ {{x=-4} \atop {y=-2}} \right.](https://tex.z-dn.net/?f=1.+%5Cleft+%5C%7B+%7B%7Bx%3D2y%7D+%5Catop+%7By%3D2%7D%7D+%5Cright.++%5Cleft+%5C%7B+%7B%7Bx%3D2%2A2%7D+%5Catop+%7By%3D2%7D%7D+%5Cright.++%5Cleft+%5C%7B+%7B%7Bx%3D4%7D+%5Catop+%7By%3D2%7D%7D+%5Cright.+%5C%5C2.+%5Cleft+%5C%7B+%7B%7Bx%3D2y%7D+%5Catop+%7By%3D-2%7D%7D+%5Cright.++%5Cleft+%5C%7B+%7B%7Bx%3D2%2A%28-2%29%7D+%5Catop+%7By%3D-2%7D%7D+%5Cright.++%5Cleft+%5C%7B+%7B%7Bx%3D-4%7D+%5Catop+%7By%3D-2%7D%7D+%5Cright.+)
Ответ(4:2) и (-4:-2)