-3х²+7х+1=-5
3х²-7х-1=5
3х²-7х-6=0
Д=49+72=121
√Д=11
х1=3
х2=-2/3
наибольшего значения нет
наименьшее значение функция принимает при х=-b/2a
при х=4/14=2/7
найдем у при этом х:
у=7·4/49-4·2/7=4/7-8/7=-4/7
Ответ: x^20+x^100-2*x^120=0
28.
1) a(b-2)/5(b-2)=a/5( b-2 сокращаем сверху и снизу)
2)3(x+4)/c(x+4)=3/c
3)ab(y+3)/a^2b(y+3)=ab/a^2b=1/a
4)15a(a-b)/20b(a-b)=15a/20b=3a/ 4b
29.
1)3a+12b/6ab=3(a+4b)/6ab=a+4b/ 2ab
3)2a-4/3(a-2)=2(a-2)/3(a-2)=2/3
5)a-3b/a^2-3ab=a-3b/a(a-3b)=1/ a
2)15b-20c/10b=5(3b-4c)/10b=3b-4c/ 2b
4)5x(y+2)/6y+12=5x(y+2)/6(y+2)=5x/ 6
6)3x^2+15xy/x+5y=3x(x+5y)/x+5y=3x
30.
1)y^2-16/3y+12=(y-4)(y+4)/3(y+4)=y-4/ 3
2)5x-15y/x^2-9y^2=5(x-3y)/(x-3y)(x+3y)=5/ x+3y
3)(c+2)^2/7c^2+14c=(c+2)^2/7c(c+2)=c+2/ 7c
4)6cd-18c/(d-3)^2=6c(d-3)/(d-3)^2=6c/ d-3
5)a^2+10a+25/a^2-25=(a+5)^2/(a-5)(a+5)==a+5/ a-5
6)y^2-9/y^2-6y+9=(y-3)(y+3)/(y-3)^2=y+3/ y-3
(/-дробь)
Длина единичной окружности: с= 2·π·1 = 2π.
4.2
Дуга АМ =
![\frac{c}{8}=\frac{2 \pi }{8}=\frac{\pi }{4}](https://tex.z-dn.net/?f=%5Cfrac%7Bc%7D%7B8%7D%3D%5Cfrac%7B2+%5Cpi+%7D%7B8%7D%3D%5Cfrac%7B%5Cpi+%7D%7B4%7D)
Дуга BD =
![\frac{c}{2}=\frac{2 \pi }{2}=\pi](https://tex.z-dn.net/?f=%5Cfrac%7Bc%7D%7B2%7D%3D%5Cfrac%7B2+%5Cpi+%7D%7B2%7D%3D%5Cpi)
Дуга CK =
![c*\frac{10}{12}=\frac{5c}{6}=\frac{5*2 \pi }{6}=\frac{5\pi }{3}](https://tex.z-dn.net/?f=c%2A%5Cfrac%7B10%7D%7B12%7D%3D%5Cfrac%7B5c%7D%7B6%7D%3D%5Cfrac%7B5%2A2+%5Cpi+%7D%7B6%7D%3D%5Cfrac%7B5%5Cpi+%7D%7B3%7D)
Дуга MP =
![c*(\frac{1}{8}+\frac{2}{12})=c*(\frac{1}{8}+\frac{1}{6})=\frac{7c}{24}=\frac{7*2 \pi }{24}=\frac{7\pi }{12}](https://tex.z-dn.net/?f=c%2A%28%5Cfrac%7B1%7D%7B8%7D%2B%5Cfrac%7B2%7D%7B12%7D%29%3Dc%2A%28%5Cfrac%7B1%7D%7B8%7D%2B%5Cfrac%7B1%7D%7B6%7D%29%3D%5Cfrac%7B7c%7D%7B24%7D%3D%5Cfrac%7B7%2A2+%5Cpi+%7D%7B24%7D%3D%5Cfrac%7B7%5Cpi+%7D%7B12%7D)
Дуга DM =
![c*\frac{3}{8}=\frac{3*2 \pi }{8}=\frac{3\pi }{4}](https://tex.z-dn.net/?f=c%2A%5Cfrac%7B3%7D%7B8%7D%3D%5Cfrac%7B3%2A2+%5Cpi+%7D%7B8%7D%3D%5Cfrac%7B3%5Cpi+%7D%7B4%7D)
Дуга MK =
![c*(\frac{1}{8}+\frac{1}{12})=\frac{5c}{24}=\frac{5*2 \pi }{24}=\frac{5\pi }{12}](https://tex.z-dn.net/?f=c%2A%28%5Cfrac%7B1%7D%7B8%7D%2B%5Cfrac%7B1%7D%7B12%7D%29%3D%5Cfrac%7B5c%7D%7B24%7D%3D%5Cfrac%7B5%2A2+%5Cpi+%7D%7B24%7D%3D%5Cfrac%7B5%5Cpi+%7D%7B12%7D)
Дуга CP =
![c*\frac{11}{12}=\frac{11*2 \pi }{12}=\frac{11\pi }{6}](https://tex.z-dn.net/?f=c%2A%5Cfrac%7B11%7D%7B12%7D%3D%5Cfrac%7B11%2A2+%5Cpi+%7D%7B12%7D%3D%5Cfrac%7B11%5Cpi+%7D%7B6%7D)
Дуга PC =
![\frac{c}{12}=\frac{2 \pi }{12}=\frac{\pi }{6}](https://tex.z-dn.net/?f=%5Cfrac%7Bc%7D%7B12%7D%3D%5Cfrac%7B2+%5Cpi+%7D%7B12%7D%3D%5Cfrac%7B%5Cpi+%7D%7B6%7D)
4.3
Дуга АМ =
![\frac{2}{5}*\frac{c}{4}=\frac{c}{10}=\frac{2 \pi }{10}=\frac{\pi }{5}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B5%7D%2A%5Cfrac%7Bc%7D%7B4%7D%3D%5Cfrac%7Bc%7D%7B10%7D%3D%5Cfrac%7B2+%5Cpi+%7D%7B10%7D%3D%5Cfrac%7B%5Cpi+%7D%7B5%7D)
Дуга МB =
![\frac{3}{5}*\frac{c}{4}=\frac{3c}{20}=\frac{3*2\pi }{20}=\frac{3\pi }{10}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B5%7D%2A%5Cfrac%7Bc%7D%7B4%7D%3D%5Cfrac%7B3c%7D%7B20%7D%3D%5Cfrac%7B3%2A2%5Cpi+%7D%7B20%7D%3D%5Cfrac%7B3%5Cpi+%7D%7B10%7D)
Дуга DМ =
![c*(\frac{1}{4}+\frac{2}{5}*\frac{1}{4})=c*(\frac{1}{4}+\frac{1}{10})=\frac{7c}{20}=\frac{7*2\pi }{20}=\frac{7\pi }{10}](https://tex.z-dn.net/?f=c%2A%28%5Cfrac%7B1%7D%7B4%7D%2B%5Cfrac%7B2%7D%7B5%7D%2A%5Cfrac%7B1%7D%7B4%7D%29%3Dc%2A%28%5Cfrac%7B1%7D%7B4%7D%2B%5Cfrac%7B1%7D%7B10%7D%29%3D%5Cfrac%7B7c%7D%7B20%7D%3D%5Cfrac%7B7%2A2%5Cpi+%7D%7B20%7D%3D%5Cfrac%7B7%5Cpi+%7D%7B10%7D)
Дуга МC =
![c*(\frac{3}{5}*\frac{1}{4}+\frac{1}{4})=c*(\frac{3}{20}+\frac{1}{4})=\frac{8c}{20}=\frac{2c}{5}=\frac{2*2\pi }{5}=\frac{4\pi }{5}](https://tex.z-dn.net/?f=c%2A%28%5Cfrac%7B3%7D%7B5%7D%2A%5Cfrac%7B1%7D%7B4%7D%2B%5Cfrac%7B1%7D%7B4%7D%29%3Dc%2A%28%5Cfrac%7B3%7D%7B20%7D%2B%5Cfrac%7B1%7D%7B4%7D%29%3D%5Cfrac%7B8c%7D%7B20%7D%3D%5Cfrac%7B2c%7D%7B5%7D%3D%5Cfrac%7B2%2A2%5Cpi+%7D%7B5%7D%3D%5Cfrac%7B4%5Cpi+%7D%7B5%7D)
Решаем квадратные уравнения ax² + bx + c = 0 с применением дискриминанта D = b² - 4ac x₁₂ = (-b +-√D)/2a
x² - 14x - 32 = 0
D=14² - 4*1*(-32) = 196 + 128 = 324 = 18²
x₁₂ = (14+-18)/2 = 16 -2
x₁ = 16
x₂ = -2
--------
-2x² + x + 15 = 0
D = 1 - 4*(-2)*15 = 1 + 120 = 121 = 11²
x₁₂ = (-1 +- 11)/2*(-2) = ( -1 +- 11)/(-4) = 3 -5/2
x₁ = 3
x₂ = -5/2