( c + 4 )( c - 4 )( c^2 + 16 ) = ( c^2 - 16 )( c^2 + 16 ) = c^4 - 256
- ( c^2 - 8 )^2 = - ( c^4 - 16c^2 + 64 ) = - c^4 + 16c^2 - 64
c^4 - 256 - c^4 + 16c^2 - 64 = 16c^2 - 320
c = - 1/4
c^2 = 1/16
16 * ( 1/16 ) - 320 = 1 - 320 = - 319
=(x -9y)/(x -3y)(x +3y) + 3y/x(x -3y) =
=(x(x -9y) +3y(x +3y)) /x(x -3y)(x +3y) =
=(x² -9xy +3xy +9y²) /x(x -3y)(x +3y) =
=(x² -6xy +9y²) /x(x -3y)(x +3y) =
=(x -3y)² /x(x -3y)(x +3y) =
=(x -3y) /x(x +3y)
3,6m + 8 - 2,4 m + 9 = 3,6m - 2,4m + 8 + 9 = 1,2 m + 17
![\displaystyle \frac{3}{cos^2(x- \frac{17 \pi }{2})}+ \frac{4}{sinx}-4=0\\\\ \frac{3}{cos^2(8 \pi + \frac{ \pi }{2}-x)}+ \frac{4}{sinx}-4=0\\\\ \frac{3}{sin^2x}+ \frac{4}{sinx}-4=0\\\\\ \frac{1}{sinx}=t\\\\3t^2+4t-4=0\\\\D=16+48=64=8^2\\\\t_{1.2}= \frac{-4\pm 8}{6}\\\\t_1=-2; t_2=2/3](https://tex.z-dn.net/?f=%5Cdisplaystyle++%5Cfrac%7B3%7D%7Bcos%5E2%28x-+%5Cfrac%7B17+%5Cpi+%7D%7B2%7D%29%7D%2B+%5Cfrac%7B4%7D%7Bsinx%7D-4%3D0%5C%5C%5C%5C+%5Cfrac%7B3%7D%7Bcos%5E2%288+%5Cpi+%2B+%5Cfrac%7B+%5Cpi+%7D%7B2%7D-x%29%7D%2B+%5Cfrac%7B4%7D%7Bsinx%7D-4%3D0%5C%5C%5C%5C+%5Cfrac%7B3%7D%7Bsin%5E2x%7D%2B+%5Cfrac%7B4%7D%7Bsinx%7D-4%3D0%5C%5C%5C%5C%5C+%5Cfrac%7B1%7D%7Bsinx%7D%3Dt%5C%5C%5C%5C3t%5E2%2B4t-4%3D0%5C%5C%5C%5CD%3D16%2B48%3D64%3D8%5E2%5C%5C%5C%5Ct_%7B1.2%7D%3D+%5Cfrac%7B-4%5Cpm+8%7D%7B6%7D%5C%5C%5C%5Ct_1%3D-2%3B+t_2%3D2%2F3++++++++)
![\displaystyle \frac{1}{sinx}=-2; sin x=- \frac{1}{2}\\\\ \frac{1}{sinx}= \frac{2}{3}; sinx= \frac{3}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle++%5Cfrac%7B1%7D%7Bsinx%7D%3D-2%3B+sin+x%3D-+%5Cfrac%7B1%7D%7B2%7D%5C%5C%5C%5C+%5Cfrac%7B1%7D%7Bsinx%7D%3D+%5Cfrac%7B2%7D%7B3%7D%3B+sinx%3D+%5Cfrac%7B3%7D%7B2%7D+++++)
во втором случае нет корней
![\displaystyle sinx=- \frac{1}{2}\\\\x=(-1)^n *arcsin(- \frac{1}{2})+ \pi n; n\in Z\\\\x_1=- \frac{ \pi }{6}+2 \pi n; n\in Z\\\\x_2=- \frac{5 \pi }{6}+2 \pi n; n\in Z](https://tex.z-dn.net/?f=%5Cdisplaystyle+sinx%3D-+%5Cfrac%7B1%7D%7B2%7D%5C%5C%5C%5Cx%3D%28-1%29%5En+%2Aarcsin%28-+%5Cfrac%7B1%7D%7B2%7D%29%2B+%5Cpi+n%3B+n%5Cin+Z%5C%5C%5C%5Cx_1%3D-+%5Cfrac%7B+%5Cpi+%7D%7B6%7D%2B2+%5Cpi+n%3B+n%5Cin+Z%5C%5C%5C%5Cx_2%3D-+%5Cfrac%7B5+%5Cpi+%7D%7B6%7D%2B2+%5Cpi+n%3B+n%5Cin+Z+++)
выбор корней на промежутке
![\displaystyle [- \frac{7 \pi }{2};-2 \pi ]](https://tex.z-dn.net/?f=%5Cdisplaystyle+%5B-+%5Cfrac%7B7+%5Cpi+%7D%7B2%7D%3B-2+%5Cpi+%5D+)
промежуток находится на втором обороте в отрицательную сторону
значит
![\displaystyle x_1=- \frac{ \pi }{6}-2 \pi =- \frac{13 \pi }{6}\\\\\ x_2=- \frac{5 \pi }{6}-2 \pi =- \frac{17 \pi }{6}](https://tex.z-dn.net/?f=%5Cdisplaystyle+x_1%3D-+%5Cfrac%7B+%5Cpi+%7D%7B6%7D-2+%5Cpi+%3D-+%5Cfrac%7B13+%5Cpi+%7D%7B6%7D%5C%5C%5C%5C%5C+x_2%3D-+%5Cfrac%7B5+%5Cpi+%7D%7B6%7D-2+%5Cpi+%3D-+%5Cfrac%7B17+%5Cpi+%7D%7B6%7D++++)