<span>8*sinx/2*cosx/2*cosx*cos2x=1
4*2*</span><span>sinx/2*cosx/2*cosx*cos2x=1
4*sinx*cosx*cos2x=1
2*sin2x*cos2x=1
sin4x=sin(</span>π/2<span>)
4x=</span>π/2
x=π/8
X²-49+40<0
x²-9<0
(x-3)(x+3)<0
x=3 x=-3
x∈(-3;3)
ОДЗ
{ x < 5
{ x < ∛35 ≈ 3,27 => x < ∛35
lg (35 - x^3) = lg (5 - x)^3
35 - x^3 = (5 - x)^3
35 - x^3 - (5 - x)^3 = 0
35 - x^3 + (x - 5)^3 = 0
35 - x^3 + (x^3 - 15x^2 + 75x - 125) = 0
- 15x^2 + 75x - 90 = 0
15x^2 - 75x + 90 = 0 /:15
x^2 - 5x + 6 = 0
D = 1
x1 = 2 ∈ ОДЗ
x2 = 3 ∈ ОДЗ
Ответ
2; 3