1) Cosx = t
6t² + t -1 = 0
D = b² -4ac = 1 - 4*6*(-1) = 25 > 0
t₁ = (-1+5)/12 = 4/12 = 1/3
t₂ = (-1 -5)/12 = -1/2
a) Cosx = 1/3 б) Сosx = -1/2
x = +-arcCos(1/3) + 2πk , k ∈Z x = +-arcCos(-1/2) + 2πn , n ∈Z
x = +- 2π/3 +2πn , n ∈ Z
2) учтём, что Cosx = 2Cos²x/2 -1
наше уравнение:
Cosx/2 = 1 + 2Cos²x/2 -1
Cosx/2 = t
2Cos²x/2 - Cosx/2 = 0
Cosx/2(2Cosx/2 -1) = 0
Cosx/2 = 0 или 2Cosx/2 -1 = 0
x/2 = π/2 + 2πk , k ∈Z Cosx/2 = 1/2
x = π + 4πk , k ∈ Z x/2 = +-arcCos(1/2) + 2πn , n ∈ Z
x/2= +- π/3+ 2πn , n ∈ Z
x = +-2π/3 + 4 πn , n ∈ Z
1) a) 4+12x+9x2
4+12x+18
22+12x
2(11+6x)
б) 25-40х+16х2
25-40х+32
57-40х
г) -56а+49а*2+16
-56а+98а+16
42а+16
2(21а+8)
2) a) (y-1)(y+1) б) p^2-9 г) (3x-2)(3x+2) д) (3x)^2-2^2 е) a^2-3^2
y^2-1 (3x)^2-2^2 9x^2-4 a^2-9
в) 4^2-(5y^2) 9x^2-4
16-25y^2
4) a) a3-b3 б) 27a3+8b3
3(a-b) 81a+24b
3(27a+8b)
Объяснение:
формула: