125
1. х² + 5х – 14 = 0
а = 1, b = 5, c = -14
D = b² – 4ac = 5² – 4•(–14)•1 = 25 + 56 = 81 = 9²
2. х² – 14х + 40 = 0
a = 1, b = -14, c = 40
D = (-14)² - 4•40•1 = 196 – 160 = 36 = 6²
3. 3у² - 13у + 4 = 0
a = 3, b = -13, c = 4
D = (-13)² - 4•3•4 = 169 – 48 = 121 = 11²
4. 12m² + m - 6 = 0
a = 12, b = 1, c = -6
D = 1² - 4•12•(-6) = 1 + 288 = 289 = 17²
5. x² + 6x - 2 = 0
a = 1, b = 6, c = -2
D = 6² – 4•1•(-2) = 36 + 8 = 44 = √44
6. 3x² - 4x - 5 = 0
a = 3, b = -4, c = -5
D = (-4)² – 4•3•(-5) = 16 + 60 = 76 = √76
7. 25x² + 60x + 36 = 0
a = 25, b = 60, c = 36
D = 60² – 4•25•36 = 3600 – 3600 = 0
8. x² - 8x + 18 = 0
a = 1, b = -8, c = 18
D = (-8)² – 4•18•1 = 64 - 72 = -8
Нет корней
126
1. (4х + 1)(х - 3) = 12
4х² - 12х + х - 3 = 12
4х² - 11х - 15 = 0
a = 4, b = -11, c = -15
D = (-11)² – 4•4•(-15) = 121 + 240 = 361 = 19
2. (x + 2)(x - 3) – (2x - 5)(x+3) = x(x-5)
x² - 3x + 2x - 6 – 2x² - 6x + 5x + 15 – x² + 5x = 0
–2x² + 3x + 9 = 0
a = -2, b = 3, c = 9
D = 3² – 4•9•(-2) = 9 + 72 = 81 = 9²
3. (6x - 5)² + (3x - 2)(3x + 2) = 36
((6x)² - 2•6x•5 + 5²) + (9x² - 4) = 36
36x² – 60x + 25 + 9x ² – 4 – 36 = 0
3x² – 4x = 0
x (3x – 4) = 0
x = 0 или 3х – 4 = 0
Объяснение:
Собственная скорость Vc= х км/ч.
Против течения :
t₁ = S/(Vc- Vт) = 18 / (x-3) (ч.)
По течению:
t₂= S/ (Vc+Vт) = 48/ (x+3) (ч.)
Всего:
t₁+t₂=3 (ч.)
18/(х-3) + 48/(х+3) = 3 |× (x-3)(x+3)
18(x+3) + 48(x-3) = 3(x-3)(x+3)
18x+54 + 48x - 144= 3(x²-9)
66x -90 = 3x² - 27 |÷3
22x - 30 = x²-9
x²-9 -22x+30=0
x²-22x+21=0
D= (-22)² -4*1*21 = 484-84=400 ; √D= 20
x₁= (22 -20) /2 =2/2=1 - не удовл. условию, т.к. скорость лодки не может быть меньше течения реки
x₂= (22+20)/2= 42/2=21 (км/ч) Vc
ответ: Vc= 21 км/ч.
125
1. х² + 5х – 14 = 0
а = 1, b = 5, c = -14
D = b² – 4ac = 5² – 4•(–14)•1 = 25 + 56 = 81 = 9²
2. х² – 14х + 40 = 0
a = 1, b = -14, c = 40
D = (-14)² - 4•40•1 = 196 – 160 = 36 = 6²
3. 3у² - 13у + 4 = 0
a = 3, b = -13, c = 4
D = (-13)² - 4•3•4 = 169 – 48 = 121 = 11²
4. 12m² + m - 6 = 0
a = 12, b = 1, c = -6
D = 1² - 4•12•(-6) = 1 + 288 = 289 = 17²
5. x² + 6x - 2 = 0
a = 1, b = 6, c = -2
D = 6² – 4•1•(-2) = 36 + 8 = 44 = √44
6. 3x² - 4x - 5 = 0
a = 3, b = -4, c = -5
D = (-4)² – 4•3•(-5) = 16 + 60 = 76 = √76
7. 25x² + 60x + 36 = 0
a = 25, b = 60, c = 36
D = 60² – 4•25•36 = 3600 – 3600 = 0
8. x² - 8x + 18 = 0
a = 1, b = -8, c = 18
D = (-8)² – 4•18•1 = 64 - 72 = -8
Нет корней
126
1. (4х + 1)(х - 3) = 12
4х² - 12х + х - 3 = 12
4х² - 11х - 15 = 0
a = 4, b = -11, c = -15
D = (-11)² – 4•4•(-15) = 121 + 240 = 361 = 19
2. (x + 2)(x - 3) – (2x - 5)(x+3) = x(x-5)
x² - 3x + 2x - 6 – 2x² - 6x + 5x + 15 – x² + 5x = 0
–2x² + 3x + 9 = 0
a = -2, b = 3, c = 9
D = 3² – 4•9•(-2) = 9 + 72 = 81 = 9²
3. (6x - 5)² + (3x - 2)(3x + 2) = 36
((6x)² - 2•6x•5 + 5²) + (9x² - 4) = 36
36x² – 60x + 25 + 9x ² – 4 – 36 = 0
3x² – 4x = 0
x (3x – 4) = 0
x = 0 или 3х – 4 = 0
Объяснение:
Собственная скорость Vc= х км/ч.
Против течения :
t₁ = S/(Vc- Vт) = 18 / (x-3) (ч.)
По течению:
t₂= S/ (Vc+Vт) = 48/ (x+3) (ч.)
Всего:
t₁+t₂=3 (ч.)
18/(х-3) + 48/(х+3) = 3 |× (x-3)(x+3)
18(x+3) + 48(x-3) = 3(x-3)(x+3)
18x+54 + 48x - 144= 3(x²-9)
66x -90 = 3x² - 27 |÷3
22x - 30 = x²-9
x²-9 -22x+30=0
x²-22x+21=0
D= (-22)² -4*1*21 = 484-84=400 ; √D= 20
x₁= (22 -20) /2 =2/2=1 - не удовл. условию, т.к. скорость лодки не может быть меньше течения реки
x₂= (22+20)/2= 42/2=21 (км/ч) Vc
ответ: Vc= 21 км/ч.