Троє друзів придбали квитки на літак в одному ряді крісел із трьох мість і випадковим чином зайняли ці місця. Знайдіть імовірність того, що кожний із друзів зайняв своє місце

X^2 - 2(a-1)x + (2a+1) = 0
1) Если оно имеет действительные корни, то D >= 0
D/4 = (b/2)^2 - ac = (a-1)^2 - 1(2a+1) = a^2 - 2a + 1 - 2a - 1 = a^2 - 4a >= 0
a(a - 4) >= 0
a <= 0 U a >= 4

Знаки корней.
2) Если a <= 0, то a - 1 < 0
x1 = (-b/2 - √(D/4)) / a = (a - 1 - √(a^2 - 4a)) / 1 = a - 1 - √(a^2 - 4a) < 0
x2 = (-b/2 + √(D/4)) / a = (a - 1 + √(a^2 - 4a)) / 1 = a - 1 + √(a^2 - 4a)
x2 может быть и больше и меньше 0.
a) a - 1 + √(a^2 - 4a) < 0
√(a^2 - 4a) < 1 - a
a^2 - 4a < a^2 - 2a + 1
2a > -1;
-1/2 < a <= 0
b) a - 1 + √(a^2 - 4a) > 0
Аналогично получаем
a < -1/2

3) Если a = -1/2, то c = 2a + 1 = 0, тогда
x^2 - 2(-1/2 + 1)x + 0 = 0
x^2 - 2(1/2)x = 0
x^2 - x = 0
x1 = 0, x2 = 1 > 0

4) Если a >= 4, то a - 1 > 0
x1 = (-b/2 - √(D/4)) / a = (a - 1 - √(a^2 - 4a)) / 1 = a - 1 - √(a^2 - 4a)
x1 может быть и больше и меньше 0.
x2 = (-b/2 + √(D/4)) / a = (a - 1 + √(a^2 - 4a)) / 1 = a - 1 + √(a^2 - 4a) > 0
a) a - 1 - √(a^2 - 4a) < 0
√(a^2 - 4a) > a - 1
a^2 - 4a > a^2 - 2a + 1
2a < -1
a < -1/2 - не подходит, потому что a >= 4
b) a - 1 - √(a^2 - 4a) >= 0
√(a^2 - 4a) <= a - 1
a^2 - 4a <= a^2 - 2a + 1
2a >= -1
a >= -1/2 - подходит для любых a >= 4
Значит, при любом a >= 4 оба корня положительны.
ответ: При -1/2 < a <= 0 будет x1 < 0, x2 < 0
При a = -1/2 будет x1 = 0, x2 > 0
При a < -1/2 будет x1 < 0, x2 > 0
При a >= 4 будет x1 > 0, x2 > 0
При 0 < a < 4 действительных корней нет.

Unit 4 Eating Out

Match the words in A with its explanation in B

1.a quality a) no good

2. abundant b) large quantities

3. customary c) to add to a dish to make it look

attractive

4. distinctive d) how good or bad something is

5. to garnish e) quickly

6.interior f) usual

7. inferior g) inside of building

8. relatively h) usual

9. rapidly i)comparatively

II. Complete the sentences with the above words:

1. design is the art of planning the decoration of the inside a house or an

office

4. These shoes are f good .

5. She made progess and was soon the best in the class.

6. thedi with parsley and serve!

7. We look a supply of food with us when we went hiking in the

mountains

8. He’s a good tennis player.

9. This sauce has a very taste.

Объяснение: Unit 4 Eating Out

Match the words in A with its explanation in B

1.a quality a) no good

2. abundant b) large quantities

3. customary c) to add to a dish to make it look

attractive

4. distinctive d) how good or bad something is

5. to garnish e) quickly

6.interior f) usual

7. inferior g) inside of building

8. relatively h) usual

9. rapidly i)comparatively

II. Complete the sentences with the above words:

1. design is the art of planning the decoration of the inside a house or an

office.

2. It’s to hold the door open for someone who is entering a building

behind you.

3. They were very upset. They had bought goods of quality.

4. These shoes are of good .

5. She made progress and was soon the best in the class.

6. the dish with parsley and serve!

7. We look an supply of food with us when we went hiking in the

mountains.

8. He’s a good tennis player.

9. This sauce has a very taste.