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2.
x² - x - 2 = 0
D = 1 - 4*1*(-2) = 1 + 8 = 9
√D = 3
x₁ = (1-3)/2 = -2/2 = -1
x₂ = (1+3)/2 = 4/2 = 2

Ответ: -1; 2

x² - 5x + 4 = 0
D = 25 - 4*1*4 = 25 - 16 = 9
√D = 3
x₁ = (5-3)/2 = 2/2 = 1
x₂ = (5+3)/2 = 8/2 = 4

Ответ: 1; 4

7x² - x - 6 = 0
D = 1 - 4*7*(-6) = 1 + 168 = 169
√D = 13
x₁ = (1-13)/14 = -12/14 = -6/7
x₂ = (1+13)/14 = 14/14 = 1

Ответ: -6/7; 1

3)
4x - 12 ≤ 2x + 7
4x - 2x ≤ 7 + 12
2x ≤ 19
x ≤ 19/2
x ≤ 9.5

Ответ: (-∞; 9.5]

3x + 5 > 4x - 1
3x - 4x > -1 - 5
-x > -6
x < 6

Ответ: (-∞; 6)

4)
cos(π - α) * sin(π/2 - α) - sin²(-α) = -cosα * cosα - sin²α = -cos²α - sin²α = - (cos²α + sin²α) = -1

sin²(π/2 - α) - sin²(π - α) = cos²α - sin²a = cos2α

(sin8α + sin2α)/(cos8α + cos2α) = [ 2sin((8a+2a)/2) * cos((8a-2a)/2) ] / [ 2cos((8a+2a)/2) * cos((8a-2a)/2) ] = (sin5α * cos3α) / (cos5α * cos3α) = sin5α/cos5α = tg5α

5(1)
a ∈ (0; π/2) ⇒ cosa > 0
cosa = √(1-sin²a) = √(1-4/9) = √5/3

sin2a = 2sinacosa = 2 * 2/3 * √5/3 = 4√5/9

6(2)
sin2a/2cos²a = 2sinacosa/2cos²a = sina/cosa = tga

ctg²a(1 - cos2a)² = ctg²a(1 - cos²a + sin²a)² = ctg²a(sin²a + sin²a)² = ctg²a(2sin²a)² = cos²a/sin²a * 4sin⁴a = 4cos²asin⁴a/sin²a = 4cos²asin²a = (2sinacosa)² = sin²2a