-x²=36+12x
-x²-12x-36=0
x²+12x+36=0
x=-6
4x-x²=7
x²-4x+7=0
D=16-28= -12
Нет корней
-4x-x²-25=20x
x²+4x+20x+25=0
x²+24x+25=0
x1= -25
x2=1
Log0.532 = -0.274
воот ответ -0.274
![\displaystyle ODZ: cosx\neq 0; cos2x\neq0\\\\x\neq \frac{\pi}{2}+\pi n ; x\neq \frac{\pi}{4}+\frac{\pi n}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle+ODZ%3A+cosx%5Cneq+0%3B+cos2x%5Cneq0%5C%5C%5C%5Cx%5Cneq+%5Cfrac%7B%5Cpi%7D%7B2%7D%2B%5Cpi+n+%3B+x%5Cneq+%5Cfrac%7B%5Cpi%7D%7B4%7D%2B%5Cfrac%7B%5Cpi+n%7D%7B2%7D)
рассмотрим два случая
sinx≥0; 2πn≤x≤π+2πn; n∈Z
![\displaystyle \frac{sinx+sin3x}{cosx*cos2x}=\frac{2}{\sqrt{3}}\\\\\frac{2sin2x*cosx}{cosx*cos2x}=\frac{2}{\sqrt{3}}\\\\tg2x=\frac{1}{\sqrt{3}}\\\\2x=\frac{\pi}{6}+\pi n; n\in Z\\\\x=\frac{\pi}{12}+\frac{\pi n}{2}; n\in Z](https://tex.z-dn.net/?f=%5Cdisplaystyle+%5Cfrac%7Bsinx%2Bsin3x%7D%7Bcosx%2Acos2x%7D%3D%5Cfrac%7B2%7D%7B%5Csqrt%7B3%7D%7D%5C%5C%5C%5C%5Cfrac%7B2sin2x%2Acosx%7D%7Bcosx%2Acos2x%7D%3D%5Cfrac%7B2%7D%7B%5Csqrt%7B3%7D%7D%5C%5C%5C%5Ctg2x%3D%5Cfrac%7B1%7D%7B%5Csqrt%7B3%7D%7D%5C%5C%5C%5C2x%3D%5Cfrac%7B%5Cpi%7D%7B6%7D%2B%5Cpi+n%3B+n%5Cin+Z%5C%5C%5C%5Cx%3D%5Cfrac%7B%5Cpi%7D%7B12%7D%2B%5Cfrac%7B%5Cpi+n%7D%7B2%7D%3B+n%5Cin+Z)
так как sin x≥0 то корни: х=π/12+2πn; x=7π/12+2πn; n∈Z
второй случай sinx<0; π+2πn<x<2π+2πn; n∈Z
![\displaystyle \frac{sin3x-sinx}{cosx*cos2x}=\frac{2}{\sqrt{3}}\\\\\frac{2cos2x*sinx}{cosx*cos2x}=\frac{2}{\sqrt{3}}\\\\tgx=\frac{1}{\sqrt{3}}\\\\x=\frac{\pi }{6}+\pi n; n\in Z](https://tex.z-dn.net/?f=%5Cdisplaystyle+%5Cfrac%7Bsin3x-sinx%7D%7Bcosx%2Acos2x%7D%3D%5Cfrac%7B2%7D%7B%5Csqrt%7B3%7D%7D%5C%5C%5C%5C%5Cfrac%7B2cos2x%2Asinx%7D%7Bcosx%2Acos2x%7D%3D%5Cfrac%7B2%7D%7B%5Csqrt%7B3%7D%7D%5C%5C%5C%5Ctgx%3D%5Cfrac%7B1%7D%7B%5Csqrt%7B3%7D%7D%5C%5C%5C%5Cx%3D%5Cfrac%7B%5Cpi+%7D%7B6%7D%2B%5Cpi+n%3B+n%5Cin+Z)
так как sinx<0 то корни х= 7π/6+2πn; n∈Z
Выборка корней на промежутке [π/2; 3π/2}
x= 7π/12; 7π/6
(3m-2) во 2-й степени -2(m-2)(m-3)+(2m-1)(2m+1)= 9m (m во второй степени, только m) -6m+4-2m (m во второй степени, только m) +6m+4m-12+4m (m во второй степени, только m) +2m-2m-1=11m(m во второй степени, только m)+6m+3
P.S Вроде так. Проверь :)