Одз y≠2
![\frac{y-14}{ y^{3} -8} = \frac{5}{y^2+2y+4} - \frac{1}{y-2} \\ y-14=5y-y^2-2y-4 \\ y^2-2y=0 \\ y(y-2)=0 \\ y_{1} =0 \\ y_{2} =2 \\](https://tex.z-dn.net/?f=+%5Cfrac%7By-14%7D%7B+y%5E%7B3%7D+-8%7D+%3D+%5Cfrac%7B5%7D%7By%5E2%2B2y%2B4%7D+-+%5Cfrac%7B1%7D%7By-2%7D+%5C%5C+y-14%3D5y-y%5E2-2y-4+%5C%5C+y%5E2-2y%3D0+%5C%5C+y%28y-2%29%3D0+%5C%5C+y_%7B1%7D+%3D0+%5C%5C+y_%7B2%7D+%3D2+%5C%5C+)
y=2 не подходит по одз
y=0
среднее арифметическое корней =0
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одз x≠1
![5x=6+ \frac{4}{x-1} \\ 5x(x-1)=6(x-1)+4 \\ 5x^2-11x+2=0 \\ D=81 \\ x_{1} =2 \\ y_{1} =10 \\ x_{2} = \frac{1}{5} \\ y_{2} =1 \\](https://tex.z-dn.net/?f=5x%3D6%2B+%5Cfrac%7B4%7D%7Bx-1%7D+%5C%5C+5x%28x-1%29%3D6%28x-1%29%2B4+%5C%5C+5x%5E2-11x%2B2%3D0+%5C%5C+D%3D81+%5C%5C+x_%7B1%7D+%3D2+%5C%5C+y_%7B1%7D+%3D10+%5C%5C+x_%7B2%7D+%3D+%5Cfrac%7B1%7D%7B5%7D+%5C%5C+y_%7B2%7D+%3D1+%5C%5C+)
ответ (2;10) (1/5;1)
#2
(80×3)+(80×3)=240+240=480 (км)
#3
2p-(3p-2p+c)=2p-3p+2-c
Функция возрастает на промежке, где ее производная больше нуля.
![y = sin( \frac{ \pi }{6} + \frac{x}{3} ) \\ y'= \frac{1}{3} cos( \frac{ \pi }{6} + \frac{x}{3} ) \\ \frac{1}{3} cos( \frac{ \pi }{6} + \frac{x}{3} )\ \textgreater \ 0 \\ cos( \frac{ \pi }{6} + \frac{x}{3} )\ \textgreater \ 0](https://tex.z-dn.net/?f=y+%3D+sin%28+%5Cfrac%7B+%5Cpi+%7D%7B6%7D+%2B+%5Cfrac%7Bx%7D%7B3%7D+%29+%5C%5C+y%27%3D++%5Cfrac%7B1%7D%7B3%7D+cos%28+%5Cfrac%7B+%5Cpi+%7D%7B6%7D+%2B+%5Cfrac%7Bx%7D%7B3%7D+%29+%5C%5C+%5Cfrac%7B1%7D%7B3%7D+cos%28+%5Cfrac%7B+%5Cpi+%7D%7B6%7D+%2B+%5Cfrac%7Bx%7D%7B3%7D+%29%5C+%5Ctextgreater+%5C+0+%5C%5C+cos%28+%5Cfrac%7B+%5Cpi+%7D%7B6%7D+%2B+%5Cfrac%7Bx%7D%7B3%7D+%29%5C+%5Ctextgreater+%5C+0)
π/6 + x/3 ∈ (-π/2 + 2πn; π/2 + 2πn), n ∈ Z
x/3 ∈ (-2π/3 + 2πn; π/3 + 2πn), n ∈ Z
x ∈ (-2π + 2πn; π + 2πn), n ∈ Z
Функция возрастает при x ∈ (-2π + 2πn; π + 2πn), n ∈ Z.