Դասարանական առաջադրանքներ՝ 192-ա,գ; 194-ա,գ; 196-ա,գ; 197-ա,գ
Վարժ 192
ա) 2x – 3 ≤ 0
2x ≤ 3
x ≤ 3/2
x∈ (-∞ ; 3/2)
բ) 4x – 3 ≥ 0
4x ≥ 3
x ≥ 3/4
x∈ (-∞ ; 3/4)
գ) 5x – 8 ≥ 3x – 1
5x – 3x ≥ 8-1
2x ≥ 7
x ≥ 7/2
x∈ (7/2,+ ∞)
դ) 2x – 4 ≤ 4x – 5
2x – 4x ≤ -5 + 4
-2x ≤ -1
x ≤ 1/2
x ≤ 0,5:
Վարժ 194
ա) -x2 + 2x – 1 ≥ 0
-x2 + 2x – 1 = 0
D = 22 – 4 x (-1) * (-1) = 4 – 4 = 0
x0 = -2/2 = -1
բ) -x2 + 4x – 4 < 0
-x2 + 4x – 4 = 0
D = 42 – 4 x (-1) x (-1) = 16
x1 = -4 – √16/2 = -4 -4/2 = -8/2 = -4
x2 = -4 + √16/2 = -4 + 4 = 2 = 0:
Վարժ 196
ա) (x2-1) (x+3) > 0
x2 – 1 = 0
x2 = 1
x = ±1
x + 3 = 0
x = -3
x∈ (-3 ; -1) U (1 ; -∞)
բ) (7 – x) (4 – x2) < 0
7 – x = 0
x = -7
4 – x2 = 0
x = ±4
գ) (12 – 5x) (x2 – 4x + 4) > 0
12 – 5x = 0
x = -2,4
x2 – 4x + 4 = 0
D = 42 – 4 x 1 x 4 = 16 – 16 = 0
x0 = -4/2 = -2
դ) (x2 – 5x + 6) (x – 3) < 0
x – 5x + 6 = 0
D = 52 – 4 * 1 * 6 = 25 – 24 = 1
x1 = -5 – √1/2 = -6/2 = -3
x2= -5 + √1/2 = -4/2 =-2:
Վարժ 197
ա) 1/x – 2 > 0
x – 1 ≠ 0
x ≠ 1
բ) 5/2 – x < 0
2 – x ≠ 0
x ≠ -2
գ) x – 8/2x + 3 > 0
x – 8 = 0
x = 8
2x + 3 ≠ 0
x ≠ -3/2
դ) 3/4x/5 + x < 0
3 – 4x = 0
x = -3/4
5 + x ≠ 0
x ≠ -5: