1)2*1/4=2/1*1/4=2/4=1/2
2)3/2-1/2=2/2=1
3)1/4*1=1/4
![1) 5^{x+1} + 5 ^{x} +5^ {x-1} = 155;\\ 5^x(5+1+5^{-1})=155\\ 5^x(6+\frac{1}{5})=155\\ 5^x*\frac{31}{5}=155 \ |*5\\ 5^x*31=775\\ 5^x=755:31\\ 5^x=25\\ 5^x=5^2\\ x=2](https://tex.z-dn.net/?f=1%29+5%5E%7Bx%2B1%7D+%2B+5+%5E%7Bx%7D+%2B5%5E+%7Bx-1%7D+%3D+155%3B%5C%5C+5%5Ex%285%2B1%2B5%5E%7B-1%7D%29%3D155%5C%5C+5%5Ex%286%2B%5Cfrac%7B1%7D%7B5%7D%29%3D155%5C%5C+5%5Ex%2A%5Cfrac%7B31%7D%7B5%7D%3D155+%5C+%7C%2A5%5C%5C+5%5Ex%2A31%3D775%5C%5C+5%5Ex%3D755%3A31%5C%5C+5%5Ex%3D25%5C%5C+5%5Ex%3D5%5E2%5C%5C+x%3D2)
Ответ: 2
![2) (log_ 2 x)^2 -3log _2 x + 2 = 0\\ log_2x=y\\ y^2-3y+2=0\\ D=(-3)^2-4*1*2=9-8=1\\ y_1=\frac{3+1}{2}=2\\ y_2=\frac{3-1}{2}=1\\ \\ log_2x=2\\ x=2^2\\ x=4\\ \\ log_2x=1\\ x=2^1\\ x=2](https://tex.z-dn.net/?f=2%29+%28log_+2+x%29%5E2+-3log+_2+x+%2B+2+%3D+0%5C%5C+log_2x%3Dy%5C%5C+y%5E2-3y%2B2%3D0%5C%5C+D%3D%28-3%29%5E2-4%2A1%2A2%3D9-8%3D1%5C%5C+y_1%3D%5Cfrac%7B3%2B1%7D%7B2%7D%3D2%5C%5C+y_2%3D%5Cfrac%7B3-1%7D%7B2%7D%3D1%5C%5C+%5C%5C+log_2x%3D2%5C%5C+x%3D2%5E2%5C%5C+x%3D4%5C%5C+%5C%5C+log_2x%3D1%5C%5C+x%3D2%5E1%5C%5C+x%3D2)
ответ: 2 или 4
![cosx + cos2x = 0\\ cos2x=2cos^2x-1\\ cosx+2cos^2 x-1=0 \\ cosx=t\\ 2t^2+t-1=0\\ D=1^2-4*2*(-1)=1+8=9\\ t_1=\frac{-1+3}{4}=\frac{1}{2}=0.5\\ t_2=\frac{-1-3}{4}=-1\\ \\ cosx=\frac{1}{2}\\ x=б \frac{\pi}{3}+2\pi n, \ \ nEZ\\ \\ cosx=-1\\ x=\pi+2\pi n , \ \ nEZ](https://tex.z-dn.net/?f=cosx+%2B+cos2x+%3D+0%5C%5C+cos2x%3D2cos%5E2x-1%5C%5C+cosx%2B2cos%5E2+x-1%3D0+%5C%5C+cosx%3Dt%5C%5C+2t%5E2%2Bt-1%3D0%5C%5C+D%3D1%5E2-4%2A2%2A%28-1%29%3D1%2B8%3D9%5C%5C+t_1%3D%5Cfrac%7B-1%2B3%7D%7B4%7D%3D%5Cfrac%7B1%7D%7B2%7D%3D0.5%5C%5C+t_2%3D%5Cfrac%7B-1-3%7D%7B4%7D%3D-1%5C%5C+%5C%5C+cosx%3D%5Cfrac%7B1%7D%7B2%7D%5C%5C+x%3D%D0%B1+%5Cfrac%7B%5Cpi%7D%7B3%7D%2B2%5Cpi+n%2C+%5C+%5C+nEZ%5C%5C+%5C%5C+cosx%3D-1%5C%5C+x%3D%5Cpi%2B2%5Cpi+n+%2C+%5C+%5C+nEZ)
P.S. Задание надо писать более понятней..... честно говоря я догадывалась
<span>3sin2x - 8 sin^2x =7
</span><span>3</span>*2sincosx - 8 sin^2x - 7 sin^2x - 7 cos^2x = 0
6sinxcosx - 15sin^2x - 7cos^2x = 0 /:(-1)
15sin^2x - 6sinxcosx + 7cos^2x = 0 /:cos^2x≠0
15tg^2x - 6tgx + 7 = 0
tgx = t
15t^2 - 6t + 7 = 0
D = 36 - 4*15*7 < 0
нет решений