S = (x + 1)(x + 2)(x + 3)(x + 4) + 1

= [(x + 1)(x + 4)][(x + 2)(x + 3)] + 1

= (x^2 + 5x + 4)(x^2 + 5x +6) + 1

Đặt t = x^2 + 5x + 5 (do x ∈ Z nên t ∈ Z)

⇒ S = (t - 1)(t + 1) + 1

= t^2 - 1 + 1

= t^2 là số chính phương do t ∈ Z

⇒ S là số cp với mọi x ∈ Z (đpcm)

\(15a^{m+2}b-45a^mb\)

= \(15a^mb.a^2-15a^mb.3\)

= \(15a^mb\left(a^2-3\right)\)

= \(15a^mb\left(a-\sqrt{3}\right)\left(a+\sqrt{3}\right)\)

1. The students are gathering all inside and outside to see the exam results.

-> both

2. They couldn’t buy the most modern car and it was too expensive.

-> because

3. I can’t go out tonight because I have too many work to do.

-> much

4. Driving a car with faulty brakes are taking quite a risk.

-> is

5. While infancy, a child grows approximately half of his or her adult height.

-> During

6. We had to eat standing up because we didn’t have anything to sit, and the grass was too wet.

-> but

7. Nobody knows that his or her life will be like in ten years’ time.

-> what

8. The film doesn’t start until 7.30 so you mustn’t leave too early.

-> don't have to

9. My friend played skillful and scored the third goal for our team.

-> skillfully

10. Jane didn’t enjoy the party and so did most of her friends.

-> neither

11. We’re considering visiting that place again. (paying)

-> We're considering paying a visit to that place again.

12. If you consider her problems, it’s not surprising she’s miserable. (bear)

-> If you bear in mind her problems, it's not surprising she's miserable.

Ta có: \(\dfrac{\text{∠}A}{6}=\dfrac{\text{∠}B}{5}=\dfrac{\text{∠}C}{4}\) = k (k > 0)

⇒ ∠A = 6k; ∠B = 5k; ∠C = 4k

Do AB//CD ⇒ ∠A + ∠D = ∠B + ∠C = 180°

⇒ 6k + ∠D = 5k + 4k

⇒ ∠D = 3k

Lại có: ABCD là hình thang

⇒ ∠A + ∠B + ∠C + ∠D = 360°

⇒ 6k + 5k + 4k + 3k = 360°

⇒ 18k = 360°

⇒ k = 20°

⇒ ∠A = 120°; ∠B = 100°; ∠C = 80°; ∠D = 60°

1. It was very noisy but we continued to study our lesson.

-> Although it was very noisy, we continued to study our lesson.

2. Although Bill took a taxi, he still arrived late for the concert.

-> In spite of taking/having taken a taxi, Bill still arrived late for the concert.

3. It rained a lot but we enjoyed our holiday so much.

-> Even though it rained a lot, we enjoyed our holiday so much.

4. Although the traffic was bad, I arrived at the cinema on time.

-> Despite the bad traffic, I arrived at the cinema on time.

 5. I was very tired but I couldn’t sleep

-> I couldn’t sleep although I was very tired.

Đầu tiên bạn khai báo các biến theo đề bài, và thêm biến S = 0

Viết code input các giá trị của biến

Tạo 2 vòng lặp lồng nhau:

i = 0 -> n - 2 và j = i + 1 -> n -1

Nếu a[i] + a[j] = k thì S +=1

Sau đó output giá trị của S