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Gọi số điện thoại cần tìm là \(\overline{abcdefgh}\) Theo đề bài ta có
\(\overline{abc}+\overline{defgh}=66558\) (1)
\(\overline{abcde}+\overline{fgh}=65577\) (2)
Trừ 2 vế của (1) cho (2)
\(\Rightarrow\overline{abc}+\overline{defgh}-\overline{abcde}-\overline{fgh}=981\)
\(\Rightarrow\overline{abc}+1000x\overline{de}+\overline{fgh}-100x\overline{abc}-\overline{de}-\overline{fgh}=981\)
\(\Rightarrow999x\overline{de}-99x\overline{abc}=981\Rightarrow111x\overline{de}-11x\overline{abc}=109\) (*)
\(\Rightarrow\overline{abc}=\frac{111x\overline{de}-109}{11}=\frac{110x\overline{de}-110+\overline{de}+1}{11}=10x\overline{de}-10+\frac{\overline{de}+1}{11}\) (**)
Do \(\overline{abc}\) là số nguyên nên \(\overline{de}+1⋮11\)
Từ (1) ta thấy \(\overline{abc}\ge100\Rightarrow\overline{defgh}\le66558-100=66458\)
Mặt khác \(\overline{abc}\le999\Rightarrow\overline{defgh}\ge66558-999=65559\)
\(\Rightarrow d=6\)
\(\Rightarrow\overline{de}+1⋮11\Rightarrow\overline{de}=65\) Thay vào (**) \(\Rightarrow\overline{abc}=10x65-10+\frac{65+1}{11}=646\)
Thay các giá trị của \(\overline{abc}\) và \(\overline{de}\) vào (2) \(\Rightarrow\overline{fgh}=65577-64665=912\)
\(\Rightarrow\overline{abcdefgh}=64665912\)
TH1) Với n = 6k
ta có: \(\left(n+1\right)\left(2n+1\right)=\left(6k+1\right)\left(12k+1\right)\) không chia hết cho 6
=> Loại
TH2) Với n = 6k+1
ta có: \(\left(n+1\right)\left(2n+1\right)=\left(6k+2\right)\left(12k+3\right)⋮6\)
=> \(A=\frac{\left(6k+2\right)\left(12k+3\right)}{6}=\left(3k+1\right)\left(4k+1\right)\)là số chính phương
Lại có: ( 3k + 1 ; 4k + 1 ) = ( 3k + 1 ; k ) = ( 2k + 1 ; k ) = ( k + 1 ; k ) = ( k ; 1 ) = 1
=> 3k + 1 và 4k + 1 đồng thời là 2 số chính phương
+) Với k \(\equiv\)\(1,3,5,7\)(mod 8 ) => 4k + 1 không là số cp
+) Với k \(\equiv\)2; 4; 6 ( mod 8) => 3k + 1 không là số chính phương
=> k \(\equiv\)0 ( mod 8) => k = 8h
=> Tìm h bé nhất để 24h + 1 và 32h + 1 là số chính phương(1)
+) Với h \(\equiv\)\(3,4,6\)( mod7) => 24k + 1 không là số chính phương
+) Với h \(\equiv\)1 (mod 7 ) => 32h + 1 không là số cp
=> h \(\equiv\)0; 2; 5 (mod 7 )
=> h = 7m hoặc h = 7n + 2 hoặc h = 7t + 7 ( với m;n; t nguyên dương )
Nếu m = 1 => h = 7 => 24h + 1 = 169 và 32h + 1 = 225 là hai số chính phương và h nhỏ nhất
=> n = 6k + 1 và k = 8h = 56
=> n = 337
=> A = 38025 là số chính phương
TH3) Với n = 6k + 2
ta có: \(\left(n+1\right)\left(2n+1\right)=\left(6k+3\right)\left(12k+5\right)\)không chia hết cho 6
TH4) Với n = 6k + 3
ta có: \(\left(n+1\right)\left(2n+1\right)=\left(6k+4\right)\left(12k+7\right)\)không chia hết cho 6
TH5) Với n = 6k + 4
ta có: \(\left(n+1\right)\left(2n+1\right)=\left(6k+5\right)\left(12k+9\right)\)không chia hết cho 6
TH6) Với n = 6k + 5
ta có \(\left(n+1\right)\left(2n+1\right)=\left(6k+6\right)\left(12k+11\right)⋮6\)
=> \(A=\frac{\left(6k+6\right)\left(12k+11\right)}{6}=\left(k+1\right)\left(12k+11\right)\)
mà ( k + 1; 12k + 11 ) = 1
=> k + 1 và 12k + 11 là 2 số chính phương
tuy nhiên 12k + 11 chia 12 dư 11 mà 1 số chính phương chia 12 không dư 11
=> Trường hợp này loại
Vậy n = 337
\(x\left(x-z\right)+y\left(y-z\right)=0\)\(\Leftrightarrow\)\(x^2+y^2=z\left(x+y\right)\)
\(\frac{x^3}{z^2+x^2}=x-\frac{z^2x}{z^2+x^2}\ge x-\frac{z^2x}{2zx}=x-\frac{z}{2}\)
\(\frac{y^3}{y^2+z^2}=y-\frac{yz^2}{y^2+z^2}\ge y-\frac{yz^2}{2yz}=y-\frac{z}{2}\)
\(\frac{x^2+y^2+4}{x+y}=\frac{z\left(x+y\right)+4}{x+y}=z-x-y+\frac{4}{x+y}+x+y\ge z-x-y+4\)
Cộng lại ra minP=4, dấu "=" xảy ra khi \(x=y=z=1\)
Bn ko biết thì đừng có đăng linh tinh nhé hoktok 😋😋😋😋😋😋😋😋😋
\(\hept{\begin{cases}x+y=a\\2x-y=3\end{cases}}\Leftrightarrow x+y+2x-y=a+3\Leftrightarrow x=\frac{a+3}{3};y=a-\frac{a+3}{3}=\frac{2a-3}{3}\)
\(x>y\Leftrightarrow\frac{a+3}{3}>\frac{2a-3}{3}\Leftrightarrow a+3>2a-3\Leftrightarrow6>a\)
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Q.1: Choose the word whose underlined part is pronounced differently from the others.
6. A. played B. frightened C. excited D. bored
7. A. hand B. transport C. character D. celebration
8. A. washed B. attended C. decided D. disappointed
Q. 2: Choose the word that has a different stress pattern from the others.
9. A. traffic B. agree C. noisy D. student
10. A. listen B. visit C. borrow D. obey
Q.5: Choose the correct answer to complete each following sentence by circling A, B, C or D.
11. Lan used to ________ morning exercise when she got up early.
A. did B. does C. doing D. do
12. My father __________the bus to work every day, but I cycle.
A. catches B. drives C. goes D. runs
13. You should look right and left when you go________the road.
A. down B. across C. up D. along
14. Bus is the main public________in Viet Nam.
A. travel B. tricycle C. transport D. vehicle
15. The play was so boring. ________, Hoa saw it from beginning to end.
A. Therefore B. Despite C .However D. Although
16. She’s sure that they will find the film_________.
A. entertaining B. entertain C. entertainment D. entertained
17. – “ Do you seeing a film?” – “_________________”
A. No, I don’t it at all B. Sure. What film shall we see?
C. Who is in it? D. I’m sorry, I can’t.
18. ____________ being frightened by the images, Lan still d the film so much.
A. In spite B. Despite C. Although D. Nevertheless
19. ____________ is La Tomatina celebrated? – Every August.
A. Where B. Why C. When D. Which
20. My father d the ____________ of that singer.
A. perform B. performer C. performance D. performing
Q.4: Put the following in correct order to make a dialogue. Write your answer into the left column.
tự làm!
21._____________ 22._____________ 23._____________ 24._____________ 25._____________ 26._____________ 27._____________ 28._____________ | A. That would be perfect. Where shall we meet? B. Great. I’ll meet you guys there. C. Hey Kien! I’m going to join Thinh Temple Festival with some friends. Do you want to come? D. Sunday morning. E. Let’s meet at the school gate at nine o’clock. F. Who else is going? G. Just some of my close friends. H. When are you guys going? |
Q. 5: Read the following text carefully and choose the correct answer A, B, C, or D for each of the gaps.
Ewan McGregor was (29)_____ in Scotland in 1971. He decided to be a (30)_____when he was only nine and he (31)_____his first film in 1992. So far in his career, he has appeared (32)_____ a lot of different types of films, including comedies, musicals, dramas, and the Star Wars movies. In his career, Ewan has worked with (33)_____ Cameron Diaz and Nicole Kidman, and his films have won (34)_____ of awards. He loves acting and when he finished (35)_____ the musical, Moulin Rouge, he said, “I have never been happier to do anything in my life”.
29. A. bear B. born C. bearing D. beared
30. A. acting B. actress C. actor D. action
31. A. made B. played C. worked D. starred
32. A. at B. on C. with D. in
33. A. directors B. actors C. actresses D. writers
34. A. a lots B. lots C. much D. some
35. A. to film B. filmed C. film D. filming
Q.6: Writing
A. Rewrite these following sentences using given words.
36. What is the distance between Vinh Phuc and Ha Noi city?
=> How far is it from Vinh Phuc to Ha Noi city?
37. I often walked to school when I was a student.
=> I used to go to school when I was a student
38. Although they are short, they still love playing sports.
=> In spite of being short, they still love playing sports.
=>In spite of them shortness , they still love playing sports.
B. Make questions for the underlined parts in each following sentence:
39. It’s about 8 km from Phuc Yen town to Ha Noi.
=>How far is it from Phuc Yen town to Ha Noi.
40. Last year I went to Hai Luu Buffalo Fighting Festival with my parents.
=>Where did you go to with your parents last year?
Q.1: Choose the word whose underlined part is pronounced differently from the others.
6. A. played B. frightened C. excited D. bored
7. A. hand B. transport C. character D. celebration
8. A. washed B. attended C. decided D. disappointed
Q. 2: Choose the word that has a different stress pattern from the others.
9. A. traffic B. agree C. noisy D. student
10. A. listen B. visit C. borrow D. obey
Q.5: Choose the correct answer to complete each following sentence by circling A, B, C or D.
11. Lan used to ________ morning exercise when she got up early.
A. did B. does C. doing D. do
12. My father __________the bus to work every day, but I cycle.
A. catches B. drives C. goes D. runs
13. You should look right and left when you go________the road.
A. down B. across C. up D. along
14. Bus is the main public________in Viet Nam.
A. travel B. tricycle C. transport D. vehicle
15. The play was so boring. ________, Hoa saw it from beginning to end.
A. Therefore B. Despite C .However D. Although
16. She’s sure that they will find the film_________.
A. entertaining B. entertain C. entertainment D. entertained
17. – “ Do you seeing a film?” – “_________________”
A. No, I don’t it at all B. Sure. What film shall we see?
C. Who is in it? D. I’m sorry, I can’t.
18. ____________ being frightened by the images, Lan still d the film so much.
A. In spite B. Despite C. Although D. Nevertheless
19. ____________ is La Tomatina celebrated? – Every August.
A. Where B. Why C. When D. Which
20. My father d the ____________ of that singer.
A. perform B. performer C. performance D. performing
Q.4: Put the following in correct order to make a dialogue. Write your answer into the left column.
tự làm!
21._____________ 22._____________ 23._____________ 24._____________ 25._____________ 26._____________ 27._____________ 28._____________ | A. That would be perfect. Where shall we meet? B. Great. I’ll meet you guys there. C. Hey Kien! I’m going to join Thinh Temple Festival with some friends. Do you want to come? D. Sunday morning. E. Let’s meet at the school gate at nine o’clock. F. Who else is going? G. Just some of my close friends. H. When are you guys going? |
Q. 5: Read the following text carefully and choose the correct answer A, B, C, or D for each of the gaps.
Ewan McGregor was (29)_____ in Scotland in 1971. He decided to be a (30)_____when he was only nine and he (31)_____his first film in 1992. So far in his career, he has appeared (32)_____ a lot of different types of films, including comedies, musicals, dramas, and the Star Wars movies. In his career, Ewan has worked with (33)_____ Cameron Diaz and Nicole Kidman, and his films have won (34)_____ of awards. He loves acting and when he finished (35)_____ the musical, Moulin Rouge, he said, “I have never been happier to do anything in my life”.
29. A. bear B. born C. bearing D. beared
30. A. acting B. actress C. actor D. action
31. A. made B. played C. worked D. starred
32. A. at B. on C. with D. in
33. A. directors B. actors C. actresses D. writers
34. A. a lots B. lots C. much D. some
35. A. to film B. filmed C. film D. filming
Q.6: Writing
A. Rewrite these following sentences using given words.
36. What is the distance between Vinh Phuc and Ha Noi city?
=> How far is it from Vinh Phuc to Ha Noi city?
37. I often walked to school when I was a student.
=> I used to go to school when I was a student
38. Although they are short, they still love playing sports.
=> In spite of being short, they still love playing sports.
=>In spite of them shortness , they still love playing sports.
B. Make questions for the underlined parts in each following sentence:
39. It’s about 8 km from Phuc Yen town to Ha Noi.
=>How far is it from Phuc Yen town to Ha Noi.
40. Last year I went to Hai Luu Buffalo Fighting Festival with my parents.
=>Where did you go to with your parents last year?
hok tốt
*Ryeo*
