4:

a: Sau 2h, người 1 đi được: 6*2=12km

hiệu vận tốc của hai người là:

9-6=3km/h

Hai xe gặp nhau sau:

12/3=4h

b: Hai người gặp nhau lúc:

7h+4h=11h

c: Lúc gặp nhau thì người đi bộ đã đi được:

(11-5)*6=36km

tk ủng hộ nha mọi người

x = 4

Tk mình nha!!!>.<

\(P=\frac{x+1}{x-3}=\frac{x-3+4}{x-3}=1+\frac{4}{x-3}\)

\(P\in Z\Rightarrow4⋮x-3\Leftrightarrow x-3\inƯ_4=\left(1;-1;2;-2;4;-4\right)\)

Biến đổi A ta được :

\(A=x\left(x+11\right)\left(x+3\right)\left(x+8\right)+144\)

\(=\left(x^2+11x\right)\left(x^2+11x+24\right)+144\)

\(=\left(x^2+11x\right)^2+24\left(x^2+11x\right)+144\)

\(=\left(x^2+11x\right)^2+2.12.\left(x^2+11x\right)+12^2\)

\(=\left(x^2+11x+12\right)^2\) là một số chính phương \(\forall x\in Z\)

Vậy A là một số chính phương (đpcm)

Xin cảm ơn ạ.

\(A=x\left(x+3\right)\left(x+8\right)\left(x+11\right)+144\)

\(=x\left(x+11\right)\left(x+3\right)\left(x+8\right)+144\)

\(=\left(x^2+11\right)\left(x^2+11+24\right)+144\)

Đặt \(x^2+11=y\Rightarrow x^2+11+24=y+24\)

\(A=y\left(y+24\right)+144\)

\(=y^2+24y+144\)

\(=y^2+2.12y+144\)

=\(\left(y+12\right)^2\)

Có \(A=\left(y+12\right)^2\) là bình phương của 1 số => A là số chính phương

\(B=\left(2017+0,17-3,48\right)\times\left(0,5\times\frac{1}{5}-\frac{3}{10}\right)\)

\(B=\left(2017,17-3,48\right)\times\left(0,1-\frac{3}{10}\right)\)

\(B=2013,69\times0,03\)

\(B=60,4107\)

Mình chỉ biết làm như thế thôi

\(\left(2017+0,17-3,48\right).\left(0,5.\frac{1}{5}-\frac{3}{10}\right)\)

\(=\left(2017+\frac{17}{100}-\frac{348}{100}\right).\left(\frac{5}{10}.\frac{1}{5}-\frac{3}{10}\right)\)

\(=\left(\frac{201700}{100}+\frac{17}{100}-\frac{348}{100}\right).\left(\frac{1}{10}-\frac{3}{10}\right)\)

\(=\frac{201369}{100}.\frac{-2}{10}\)

\(=-402,738\)

Sai bet

Rewrite the sentences beginning with the words given
1- She didn’t bring her umbrella so she became wet.
If ____she had brought her umbrella, she wouldn't have become wet ________________________________________________________
2- “What is hasna doing now?”
Rim’s mother asked me what Hasna was doing then ____________________________________________________________
3- He doesn’t pay attention so he makes a lot of mistakes in the exam.
If he____paid attenton ,he wouldn't make a lot of mistakes in the exam. _______________________________________________________
4- Asmae is tired of working on weekends.
If only Asmaee weren't tired of working on weekends. ____________________________________________________________
5- “don’t go alone.it is dangerous
The policeman said to us not to go alone because it was dangerous ____________________________________________________________
6- “Were you at school last Saturday?”
The teacher asked his students___if they had been at school the previous Saturday_________________________________________________________
7- “Where did you study when you were a child?”
Mr. Smith asked me____where i had stuied when i had been a child________________________________________________________
8- It’s a pity she doesn’t live near school.
She regrets ___not living near school_________________________________________________________
9- She helped me in my studies.
I ___was helped in my studies_________________________________________________________
10- “How long have you been in this city? «Maria asked Lina.
Maria wanted to know _____how long Lina had been in that city_______________________________________________________
11- They are building shelters for the homeless people here.
Shelters ___are being built for the homeless people here. _________________________________________________________
12- Mary is very intelligent but she doesn’t get good marks.
Although______Mary is very intelligent ,she doesn’t get good marks.______________________________________________________
13- I am too busy these days.
If only _i weren't too busy these days___________________________________________________________
14- “Lend me your pen for a moment”.
I said to Khalid to lend me his pen for a moment ____________________________________________________________
15- They will invite her as a guest.
She ___will be invited as a guest_________________________________________________________
16- “Can you prepare this kind of food?”
Julia asked Khadija if he could prepare that kind of food ____________________________________________________________
17- The team played well; however, they lost the match.
In spite of ___playing well,the team lost the match_________________________________________________________
18- It’s a pity, we couldn’t visit the museum.
We wish ____we could visit the museum________________________________________________________
19- “My parents are going on a pilgrimage next month”.
Zaynab told me_____his parents were going on a pilgrimage next month_______________________________________________________
20- She became very fat because she ate a lot of sweeties.
If __she hadn't eaten a lot of swetties, she wouldn't have become very fat __________________________________________________________
21- “We haven’t found any practical solutions for this problem yet”.
The manager admitted not having found  any practical solutions for this problem yet”. ____________________________________________________________
22- Anass didn’t get the job because he was late for the interview.
If __Anass hadn't been late for the interview, he would have got the job_________________________________________________________
23- I didn’t’ know that you were in hospital, that’s why I didn’t call you.
If __i had known that you had been in hospital, i would have called you__________________________________________________________
24- I am sorry I can’t drive.
I wish _i could drive___________________________________________________________
25- “Don’t watch late-night horror film”.
I warned them__not to watch  late-night horror film __________________________________________________________
26- “What shall I do with my heavy luggage?”
She asked ___me what she should do with her heavy luggage_________________________________________________________
27- We got lost because we didn’t take a map.
We regret ___not having taken a map_________________________________________________________
28- “Are you working as well as studying?”
Peter asked the boy if he was working as well as studying ____________________________________________________________
29- Youness had a food poisoning he ate in a restaurant downtown.
He wishes ____Youness hadn't eaten in a restaurant downtown_________________________________________________

a) Gọi d là ƯCLN(n + 1, 2n + 3), d ∈ N*

\(\Rightarrow\hept{\begin{cases}n+1⋮d\\2n+3⋮d\end{cases}\Rightarrow\hept{\begin{cases}2\left(n+1\right)⋮d\\2n+3⋮d\end{cases}\Rightarrow}\hept{\begin{cases}2n+2⋮d\\2n+3⋮d\end{cases}}}\)

\(\Rightarrow\left(2n+3\right)-\left(2n+2\right)⋮d\)

\(\Rightarrow1⋮d\)

\(\Rightarrow d=1\)

\(\RightarrowƯCLN\left(n+1,2n+3\right)=1\)

\(\Rightarrow\frac{n+1}{2n+3}\) là phân số tối giản.

b) Gọi d là ƯCLN(2n + 3, 4n + 8), d ∈ N*

\(\Rightarrow\hept{\begin{cases}2n+3⋮d\\4n+8⋮d\end{cases}\Rightarrow\hept{\begin{cases}2\left(2n+3\right)⋮d\\4n+8⋮d\end{cases}\Rightarrow}\hept{\begin{cases}4n+6⋮d\\4n+8⋮d\end{cases}}}\)

\(\Rightarrow\left(4n+8\right)-\left(4n+6\right)⋮d\)

\(\Rightarrow2⋮d\)

\(\Rightarrow d\in\left\{1;2\right\}\)

Mà 2n + 3 không chia hết cho 2

\(\Rightarrow d=1\)

\(\RightarrowƯCLN\left(2n+3,4n+8\right)=1\)

\(\Rightarrow\frac{2n+3}{4n+8}\) là phân số tối giản.

c) Gọi d là ƯCLN(3n + 2, 5n + 3), d ∈ N*

\(\Rightarrow\hept{\begin{cases}3n+2⋮d\\5n+3⋮d\end{cases}\Rightarrow\hept{\begin{cases}5\left(3n+2\right)⋮d\\3\left(5n+3\right)⋮d\end{cases}\Rightarrow}\hept{\begin{cases}15n+10⋮d\\15n+9⋮d\end{cases}}}\)

\(\Rightarrow\left(15n+10\right)-\left(15n+9\right)⋮d\)

\(\Rightarrow1⋮d\)

\(\Rightarrow d=1\)

\(\RightarrowƯCLN\left(3n+2,5n+3\right)=1\)

\(\Rightarrow\frac{3n+2}{5n+3}\) là phân số tối giản.

Gọi d là ƯCLN của n + 1 , 2n + 3 

=> n + 1 chia hết cho d , 2n + 3 chia hết cho d

=> 2(n + 1)  chia hết cho d , 2n + 3 chia hết cho d

=> 2n + 2 chia hết cho d , 2n + 3 chia hết cho d

=> 2n + 3 - 2n - 2 chia HẾT CHO d

=> 1 chia hết cho d

=> d = 1

Vậy n + 1/2n + 3 tối giản với mọi số n

b,c tương tự 

HÀ THANH THẢO:

Bài này dài quá. Thôi chiều ý bạn vậy!!!

a, n + 1/ 2n + 3

Ta gọi a là ƯCLN (n + 1; 2n + 3)

Theo bài ra, ta có:

n + 1 \(⋮\)a; 2n + 3 \(⋮\)a

=> 2n + 1 chia hết cho a; 2n + 3 chia hết cho a

Ta lại có:

2n + 2 chia hết cho a; 2n + 3 chia hết cho a

=> 2n + 3 - 2n + 2 \(⋮\)a

=>  1 \(⋮\)a

Vậy a = 1

Câu b và c: bạn tự áp dụng vào:

^_^, Chúc bạn học tốt!!!

các cặp số đều bé hơn 1

Đi đâu mà vội mà vàng 

Mà vấp phải đá 

Mà quàng phải dây

Dừng chân lại tích mấy cái 

Thì may mắn cả năm.

vs A=0==>từng hạng tử trong đa thức =0

==>ta đc x=y=z=1(đpcm)

mk nhịu

a)    \(\frac{28\times7-45\times7+7\times18}{45\times14}\)

\(=\frac{7\left(28-45+7\right)}{45\times14}\)

\(=\frac{7\times\left(-10\right)}{45\times14}=\frac{-1}{9}\)

b)   \(\frac{12.3-2.6}{4.5.6}\)

\(=\frac{2.6.3-2.6}{4.5.6}\)

\(=\frac{2.6\left(3-1\right)}{2.2.5.6}\)

\(=\frac{2.6.2}{2.2.5.6}\)\(=\frac{1}{5}\)

a)\(\frac{28\times7-45\times7+7\times18}{45\times14}\)

\(=\frac{7\times\left(28-45+18\right)}{45\times14}\)

\(=\frac{7\times1}{45\times14}\)

\(=\frac{1}{90}\)

b)\(\frac{12\times3-2\times6}{4\times5\times6}\)

\(=\frac{12\times\left(3-1\right)}{4\times5\times6}\)

\(=\frac{6\times2\times2}{2\times2\times5\times6}\)

\(=\frac{1}{5}\)

P/s em tham khảo nhé