rozwiąż :
1) (3x-5)^>362) (2x+3)^ mniejsze równe 16
1.
(3x-5)²>36
9x² -30x +25 > 36
9x² - 30 x - 11 >0
a =9
b =-30
c =-11
Δ = 900+ 396 =1296
√Δ = 36
x1 =(30-36)/18 = -1/3 x2 = (30+36)/18 = 11/3
Odp: x € (-∞,-1/3) U (11/3, +∞)
2.
(2x+3)² ≤ 16
4x²+12x+9 ≤ 16
4x²+12x - 7 ≤ 0
a =4
b =12
c =-7
Δ =144 + 112 = 256
√Δ =16
x1 = (-12-16)/8 = -7/2 x2=(-12+16)/8 = 1/2
Odp: x € <-7/2 , 1/2 >
Δ=b²-4ac
x1= -b-√Δ/2a x2= -b+√Δ/2a
x € (-∞,-1/3) U (11/3, +∞)
Odp: x € <-7/2 , 1/2>
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1.
(3x-5)²>36
9x² -30x +25 > 36
9x² - 30 x - 11 >0
a =9
b =-30
c =-11
Δ = 900+ 396 =1296
√Δ = 36
x1 =(30-36)/18 = -1/3 x2 = (30+36)/18 = 11/3
Odp: x € (-∞,-1/3) U (11/3, +∞)
2.
(2x+3)² ≤ 16
4x²+12x+9 ≤ 16
4x²+12x - 7 ≤ 0
a =4
b =12
c =-7
Δ =144 + 112 = 256
√Δ =16
x1 = (-12-16)/8 = -7/2 x2=(-12+16)/8 = 1/2
Odp: x € <-7/2 , 1/2 >
1.
(3x-5)²>36
9x² -30x +25 > 36
9x² - 30 x - 11 >0
Δ=b²-4ac
Δ = 900+ 396 =1296
√Δ = 36
x1= -b-√Δ/2a x2= -b+√Δ/2a
x1 =(30-36)/18 = -1/3 x2 = (30+36)/18 = 11/3
x € (-∞,-1/3) U (11/3, +∞)
2.
(2x+3)² ≤ 16
4x²+12x+9 ≤ 16
4x²+12x - 7 ≤ 0
Δ=b²-4ac
Δ =144 + 112 = 256
√Δ =16
x1= -b-√Δ/2a x2= -b+√Δ/2a
x1 = (-12-16)/8 = -7/2 x2=(-12+16)/8 = 1/2
Odp: x € <-7/2 , 1/2>