Добавим 6х и вычтем 6х , получим
(2x^2-6x+6x-5x-3)/(x-3)=(2x(x-3)+(x-3))/(x-3)=((x-3)(2x+1))/(x-3)=2x+1
X^2+2x-3=0
Находим дискриминант:
D = 22 - 4 • 1 • (-3) = 16
Корни уравнения:
x1=(-2+4)/2=1
x2=(-2-4)/2=-3
(1- sin^4a-cos^4a)/cos^4a =
(4-3-cos4a/4) /cos^4a =
(1-cos4a)/4cos^4a =
(8cos^2a- 8 cos^4a)/4cos^4a = (2/cos^2a) -2=(2-2cos^2a)/cos^2a
cos x=t,
6t²-7t-5=0,
D=169,
t1=-½, t2=1 ⅔>1,
cos x=-½,
x=±arccos (-½) + 2πk, k∈Z,
x=±(π-arccos (½)) + 2πk, k∈Z,
x=±(π-π/3) + 2πk, k∈Z,
x=±2π/3 + 2πk, k∈Z,
-7π/2<±2π/3 + 2πk<-5π/2,
[-7π/2-2π/3<2πk<-5π/2-2π/3, -7π/2+2π/3<2πk<-5π/2+2π/3,
[-25π/6<2πk<-19π/6, -17π/6<2πk<-11π/6,
[-25/12<k<-19/12, -17/12<k<-11/12,
[k=-2, k=-1,
x=2π/3 - 4π,
x=-10π/3;
x=-2π/3-2π,
x=-8π/3.