РЕШЕНИЕ:

x²​−7x+12≥0

x²​−7x+12 = 0
D = 49 - 4∙1∙12 = 49 – 48 = 1 = 1²
x₁ = (7 + 1) / 2 = 8/2 = 4
x₂ = (7 – 1) / 2 = 6/2 = 3

Ответ: 2

РЕШЕНИЕ:

81x²​≤16

81x²​ – 16 ≤ 0

(9x – 4)(9x + 4) ≤ 0

(9x – 4)(9x + 4) = 0
9x – 4 = 0 или 9x + 4 = 0
х = 4/9
х = –4/9

Ответ: 2

РЕШЕНИЕ:

x²​−17x+72 ≤ 0

x²​−17x+72=0
D = 289 – 4∙1∙72 = 289 – 288 = 1 = 1²
x₁ = (17 + 1) / 2 = 18/2 = 9
x₂ = (17 – 1) / 2 = 16/2 = 8

Ответ: 4

РЕШЕНИЕ:

x^2​−6x−27 < 0

x^2​−6x−27 = 0
D = 36 – 4∙1∙( – 27) = 36 + 108 = 144 = 12²
x₁ = (6+12) / 2 = 18 / 2 = 9
x₂ = (6 –12) / 2 = –6 / 2 = –3

Ответ: 4

РЕШЕНИЕ:

x²​+9x+20≥0

x²​+9x+20 = 0
D = 81 - 4∙1∙20 = 81 – 80 = 1 = 1²
x₁ = ( –9 + 1) / 2 = –8/2 = –4
x₂ = ( –9 – 1) / 2 = –10/2 = –5

Ответ: 4

РЕШЕНИЕ:

x²​−2x−3≥0

x²​−2x−3 = 0
D = 4 - 4∙1∙( – 3) = 4 + 12 = 16 = 4²
x₁ = (2 + 4) / 2 = 6/2 = 3
x₂ = (2 – 4) / 2 = –2/2 = –1

Ответ: 3