Cho \(P\left(x\right)=x^4+ax^3+bx^2+cx+d\), trong đó a, b, c, d là hằng số.
Gia su \(P\left(1\right)=10,P\left(2\right)=20,P\left(3\right)=30\). Hãy tính \(\frac{P\left(12\right)+P\left(-8\right)}{10}\)
K
Khách
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BM
2
KN
25 tháng 2 2020
p là số nguyên tố lớn hơn 3 nên p có hai dạng: 3k + 1 hoặc 3k - 1.
+) Xét p = 3k + 1
*) Nếu d = 3a + 1 thì \(p+2d=3k+1+6a+2=3k+6a+3⋮3\)
Lại có: \(p+2d>3\)nên p + 2d là hợp số (vô lí)
*) Nếu d = 3a + 2 thì \(p+d=3k+1+3a+2=3k+3a+3⋮3\)
Lại có: \(p+d>3\)nên p + d là hợp số (vô lí)
Vậy d chia hết cho 3 ở trong trường hợp này.
+) Xét p = 3k - 1
*) Nếu d = 3m + 1 thì \(p+d=3k-1+3m+1=3k+3m⋮3\)
Lại có: \(p+d>3\)nên p + d là hợp số (vô lí)
*) Nếu d = 3m + 2 thì \(p+2d=3k-1+6m+4=3k+6m+3⋮3\)
Lại có: \(p+2d>3\)nên p + 2d là hợp số (vô lí)
Ở trong th này, d cũng chia hết cho 3.
Vậy d chia hết cho 3
Măt khác: d chẵn vì p và p + d lẻ (do p;p+d nguyên tố ) nên d chia hết cho 6
Vậy \(d⋮6\left(đpcm\right)\)
LA
21 tháng 4 2021
Để \(\frac{2a+2b}{ab+1}\) là bình phương của 1 số nguyên thì 2a + 2b chia hết cho ab + 1; mà ab + 1 chia hết cho 2a + 2b => ab + 1 = 2b + 2a
=> \(\frac{2a+2b}{ab+1}\)=1 = 12
HA
9 tháng 6 2020
A) XÉT \(\Delta ABC\)VUÔNG TẠI
CÓ AM LÀ TRUNG TUYẾN \(\Rightarrow AM=\frac{1}{2}BC\Leftrightarrow AM=BM=CM\)
XÉT TAM GIÁC AMC CÓ AM=CM => TAM GIÁC AMC CÂN TẠI M
MÀ TRONG TAM GIÁC CÂN ĐƯỜNG CAO CŨNG LÀ TIA PHÂN GIÁC => MH LÀ PHÂN GIÁC CỦA \(\widehat{AMC}\)
\(\Rightarrow\widehat{AMH}=\widehat{HMC}\)
XÉT \(\Delta AMH\)VÀ \(\Delta CMH\)CÓ
\(AM=MC\left(CMT\right)\)
\(\widehat{AMH}=\widehat{HMC}\left(CMT\right)\)
MH LÀ CẠNH CHUNG
=>\(\Delta AMH\)=\(\Delta CMH\)(C-G-C)
=> AH= CH ( HAI CẠNH TƯƠNG ỨNG)
=> BH LÀ ĐƯỜNG TRUNG TUYẾN CỦA TAM GIÁC ABC
VÌ HAI TĐƯỜNG TRUNG TUYẾN AM VÀ BH CẮT NHAU TẠI G
=> G LÀ TRỌNG TÂM CỦA TAM GIÁC ABC
B)
XÉT \(\Delta ABC\)VUÔNG TẠI A
CÓ AM LÀ TRUNG TUYẾN
\(\Rightarrow AM=\frac{1}{2}BC\left(Đ/L\right)\)P/S CHỈ ÁP DỤNG TRAM GIÁC GIÁC VUÔNG
3 tháng 6 2020
c) Tính chất đường trung tuyến ứng với cạnh huyền của tam giác vuông, bạn lên mạng tham khảo , EZ
a) AM = MC nên tam giác AMC cân tại M nên MH là đường cao cũng là trung tuyến hay H là trung điểm của AC nên BH là trung tuyến của tam giác ABC
Mà AM cũng là trung tuyến của tam giác ABC nên G trọng tâm của tam giác ABC
BA
11
31 tháng 8 2019
Ta có:
\(1-\frac{1}{1+2}=1-\frac{1}{2.3:2}=1-\frac{2}{6}=\frac{4}{6}=\frac{1.4}{2.3}\)
\(1-\frac{1}{1+2+3}=1-\frac{1}{3.4:2}=1-\frac{2}{12}=\frac{10}{12}=\frac{2.5}{3.4}\)
\(1-\frac{1}{1+2+3+4}=1-\frac{1}{4.5:2}=1-\frac{2}{20}=\frac{18}{20}=\frac{3.6}{4.5}\)
...
\(1-\frac{1}{1+2+3+...+2006}=1-\frac{1}{2006.2007:2}=1-\frac{2}{2006.2007}=\frac{2005.2008}{2006.2007}\)
=> \(\left(1-\frac{1}{1+2}\right).\left(1-\frac{1}{1+2+3}\right)...\left(1-\frac{1}{1+2+3+...+2006}\right)\)
\(=\frac{1.4}{2.3}.\frac{2.5}{3.4}.\frac{3.6}{4.5}.\frac{2005.2008}{2006.2007}\)
\(=\frac{\left(1.2.3....2005\right).\left(4.5.6...2008\right)}{\left(2.3.4...2006\right)\left(3.4.5...2007\right)}=\frac{1}{2006}.\frac{2008}{3}=\frac{2008}{6018}\)
26 tháng 5 2020
Một mảnh vườn hình chữ nhật có nữa chu vi 120m , chiều dài hơn chiều rộng 20m .
a) Tính diện tích mảnh vườn ình chữ nhật đó ?
b) Người ta dùng 4/7 diện tích đó đẻ trồng hoa . Hỏi diện tích trồng hoa là bao nhiêu mét vuông ?
15 tháng 8 2016
3^105 + 4^105 = 27^35 + 64^35 chia hết cho 27+64=91
Mà 91 chia hết cho 13 nên 3^105 + 4^105 chia hết cho 13
91 ko chia hết cho 11 nên 3^105+4^105 ko chia hết cho 11
DK
7
CH
Cô Hoàng Huyền
Admin
VIP
22 tháng 2 2018
Gọi N là điểm trên BC sao cho BM = MN = NC
Do tam giác ABC đều nên AB = AC và \(\widehat{A}=\widehat{B}=\widehat{C}=60^o\)
Từ đó ta có ngay \(\Delta ABM=\Delta ACN\left(c-g-c\right)\)
\(\Rightarrow\widehat{BAM}=\widehat{CAN}\) (Hai góc tương ứng)
Lấy điểm E trên tia đối tia MA sao cho ME = MA
Khi đó ta có ngay \(\Delta ABM=\Delta ENM\left(c-g-c\right)\Rightarrow AB=EN\)
Xét tam giác ABM có góc B = 60o, \(\widehat{BAM}< 30^o\) nên \(\widehat{AMB}>90^o\)
Vậy thì theo quan hệ cạnh góc trong tam giác AB > AM
Suy ra EN > AM
Lại có AM = AN nên EN > AN hay \(\widehat{MAN}>\widehat{MEN}\Rightarrow\widehat{MAN}>\widehat{BAM}\)
Ta có \(\widehat{BAM}+\widehat{MAN}+\widehat{NAC}=60^o\Rightarrow\widehat{MAN}+2\widehat{BAM}=60^o\)
mà \(\widehat{MAN}>\widehat{BAM}\Rightarrow3\widehat{BAM}< 60^o\Rightarrow\widehat{BAM}< 20^o\)
27 tháng 12 2017
A=\(\frac{2018}{2017^2+1}+\frac{2018}{2017^2+2}+..........+\frac{2018}{2017^2+2017}\)
>\(\frac{2018}{2017^2+2017}+\frac{2018}{2017^2+2017}+........+\frac{2018}{2017^2+2017}\)
\(=\frac{2018}{2017^2+2017}.2017=\frac{2018.2017}{2017\left(2017+1\right)}=1\) (1)
Lại có:A<\(\frac{2018}{2017^2+1}+\frac{2018}{2017^2+1}+.........+\frac{2018}{2017^2+1}\)
\(=\frac{2018}{2017^2+1}.2017=\frac{2018.2017}{2017^2+1}=\frac{2017.\left(2017+1\right)}{2017^2+1}\)
\(=\frac{2017^2+2017}{2017^2+1}=\frac{2017^2+1+2016}{2017^2+1}=1+\frac{2016}{2017^2+1}< 2\) (2)
Từ (1) và (2) suy ra:1 < A < 2
Vậy A không phải là số nguyên
4 tháng 5 2020
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?
4 tháng 5 2020
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*
Đặt Q(x)=P(x)-10x. Khi đó Q(1)=Q(2)=Q(3)=0
Vì vậy Q(x) chia hết cho (x-1)(x-2)(x-3). Q(x) là đa thức bậc 4 (do P(x) là đa thức bậc 4) nên Q(x)=(x-1)(x-2)(x-3)(x-r) và
P(x)=(x-1)(x-2)(x-3)(x-r)+10x
P(12)=1200-990r
P(-8)=7840+990r
Vậy \(\frac{P\left(12\right)+P\left(-8\right)}{10}=1984\)
Ta có: \(P\left(1\right)=1+a+b+c+d=10\)
\(P\left(2\right)=16+8a+4b+2c+d=20\)
\(P\left(3\right)=81+27a+9b+3c+d=30\)
và \(P\left(12\right)=20736+1728a+144b+12c+d\)
\(P\left(-8\right)=4096-512a+64b-8c+d\)
suy ra \(P\left(12\right)+P\left(-8\right)=24832+1216a+208b+4c+2d\)
Ta lại có: \(100.P\left(1\right)-198.P\left(2\right)+100.P\left(3\right)\) \(=100\left(1+a+b+c+d\right)-198\left(16+8a+4b+2c+d\right)+100\left(81+27a+9b+3c+d\right)\)
\(=100+100a+100b+100c+100d-3168-1584a-792b-396c-198d+8100+2700a+900b+300c+100d\)
\(=5032+1216a+208b+4c+2d\)
Mặt khác: \(100.P\left(1\right)-198.P\left(2\right)+100.P\left(3\right)\)
\(=100\times10-198\times20+100\times30=40\)
Do đó: \(5032+1216a+208b+4c+2d=40\)
\(\Rightarrow\)\(1216a+208b+4c+2d=40-5032=-4992\)
Thế \(1216a+208b+4c+2d=-4992\) vào \(P\left(12\right)+P\left(-8\right)=24832+1216a+208b+4c+2d\)
ta được: \(P\left(12\right)+P\left(-8\right)=24832-4992=19840\)
Vậy \(\frac{P\left(12\right)+P\left(-8\right)}{10}=\frac{19840}{10}=1984\)